1,592
个编辑
更改
跳到导航
跳到搜索
Moved page from wikipedia:en:Self-organized criticality (history)
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]]. Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.
In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.
在物理学中，自组织临界性是动力系统的一种特性，动力系统有一个临界点作为吸引子。它们的宏观行为因此显示了相变临界点的空间或时间尺度不变特性，但不需要调整控制参数到一个精确的值，因为系统有效地调整自己，因为它进化到临界状态。
The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987>
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987>
这个概念是由 Per Bak，Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的
{{cite journal
{{cite journal
{引用期刊
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| author = Bak, P., Tang, C. and Wiesenfeld, K.
作者 Bak，p. ，Tang，c. and Wiesenfeld，k。
| year = 1987
| year = 1987
1987年
| title = Self-organized criticality: an explanation of 1/''f'' noise
| title = Self-organized criticality: an explanation of 1/f noise
自组织临界性: 1 / f 噪音的解释
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 59
| volume = 59
第59卷
| issue = 4
| issue = 4
第四期
| pages = 381–384
| pages = 381–384
381-- 384
| doi = 10.1103/PhysRevLett.59.381
| doi = 10.1103/PhysRevLett.59.381
10.1103 / physrvlett. 59.381
| pmid = 10035754
| pmid = 10035754
10035754
| bibcode=1987PhRvL..59..381B
| bibcode=1987PhRvL..59..381B
| bibcode 1987PhRvL. . 59. . 381 b
}}
}}
}}
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref>
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref>
论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考
published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995>
published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995>
1987年发表在《物理评论快报》上，被认为是复杂性的机制之一
{{cite journal
{{cite journal
{引用期刊
| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]
| author = Bak, P., and Paczuski, M.
作者 Bak，p，and Paczuski，m。
| year = 1995
| year = 1995
1995年
| title = Complexity, contingency, and criticality
| title = Complexity, contingency, and criticality
| 标题复杂性、偶然性和临界性
| journal =Proc Natl Acad Sci U S A
| journal =Proc Natl Acad Sci U S A
美国科学促进协会
| volume = 92
| volume = 92
第92卷
| pages = 6689–6696
| pages = 6689–6696
6689-- 6696
| pmid = 11607561
| pmid = 11607561
11607561
| doi = 10.1073/pnas.92.15.6689
| doi = 10.1073/pnas.92.15.6689
10.1073 / pnas. 92.15.6689
| issue = 15
| issue = 15
第15期
| pmc = 41396
| pmc = 41396
41396
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85>
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85>
| bibcode 1995PNAS... 92.6689 b } / ref 在自然界中出现。它的概念已经被应用于各个领域，比如地球物理学，参考名称 smalleyturcottesolla85
{{cite journal
{{cite journal
{引用期刊
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985
1 Smalley，r. f. ，jr. | author2 Turcotte，d. l. | author3 Solla，s. a.1985年
| title = A renormalization group approach to the stick-slip behavior of faults
| title = A renormalization group approach to the stick-slip behavior of faults
| 题目: 断层粘滑行为的重整化群方法
| journal = Journal of Geophysical Research
| journal = Journal of Geophysical Research
地球物理研究期刊
| bibcode = 1985JGR....90.1894S
| bibcode = 1985JGR....90.1894S
1985JGR... 90.1894 s
| doi = 10.1029/JB090iB02p01894
| doi = 10.1029/JB090iB02p01894
| doi 10.1029 / JB090iB02p01894
| volume = 90
| volume = 90
第90卷
| issue = B2
| issue = B2
| 第二期
| pages = 1894
| pages = 1894
1894页
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001>
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001>
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学，进化生物学和生态学，生物启发计算和优化(数学) ，经济学，量子引力，社会学，太阳物理学，等离子物理学，神经生物学参考名称 linkenkaerhansen2001
{{cite journal
{{cite journal
{引用期刊
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
人类大脑振荡中的长程时间相关性和标度行为
| journal = J. Neurosci.
| journal = J. Neurosci.
作者: j. Neurosci。
| volume = 21
| volume = 21
第21卷
| pages = 1370–1377
| pages = 1370–1377
1370-- 1377
| pmid = 11160408
| pmid = 11160408
11160408
| issue = 4
| issue = 4
第四期
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003>
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003>
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003
{{cite journal
{{cite journal
{引用期刊
|author1=J. M. Beggs |author2=D. Plenz
|author1=J. M. Beggs |author2=D. Plenz
1 j.2 d.Plenz
|lastauthoramp=yes | year = 2006
|lastauthoramp=yes | year = 2006
2006年
| title = Neuronal Avalanches in Neocortical Circuits
| title = Neuronal Avalanches in Neocortical Circuits
新皮层神经回路中的神经雪崩
| journal = J. Neurosci.
| journal = J. Neurosci.
作者: j. Neurosci。
| volume = 23
| volume = 23
第23卷
|issue=35
|issue=35
第35期
|pages=11167–77
|pages=11167–77
第11167-77页
|doi=10.1523/JNEUROSCI.23-35-11167.2003
|doi=10.1523/JNEUROSCI.23-35-11167.2003
10.1523 / jneurosci. 23-35-11167.2003
|pmid=14657176
|pmid=14657176
14657176
|pmc=6741045
|pmc=6741045
6741045
}}</ref><ref name=Chialvo2004>
}}</ref><ref name=Chialvo2004>
} / ref ref name chialvo2004
{{cite journal
{{cite journal
{引用期刊
| author =Chialvo, D. R.
| author =Chialvo, D. R.
作者 Chialvo，d. r。
| year = 2004
| year = 2004
2004年
| title = Critical brain networks
| title = Critical brain networks
关键的大脑网络
| journal = Physica A
| journal = Physica A
物理学杂志 a
| volume = 340
| volume = 340
第340卷
| issue =4
| issue =4
第四期
| pages = 756–765
| pages = 756–765
756-- 765
| doi = 10.1016/j.physa.2004.05.064
| doi = 10.1016/j.physa.2004.05.064
10.1016 / j.physa. 2004.05.064
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo
}}</ref> and others.
}}</ref> and others.
} / ref and others.
SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.
SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.
Soc 是典型的多自由度、强非线性动力学的缓慢驱动非平衡系统。自从 BTW 的原始论文以来，已经确定了许多单独的例子，但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 SOC。
== Overview ==
== Overview ==
概览
Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.
Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.
自组织临界性是20世纪下半叶统计物理学及相关领域的众多重要发现之一，这些发现尤其与研究自然界的复杂性有关。例如，细胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的《生命的游戏》和 Stephen Wolfram 的大量工作---- 清楚地表明，复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内，beno t Mandelbrot 关于分形的大量工作表明，自然界的许多复杂性可以用某些无处不在的数学定律来描述，而在20世纪60年代和70年代对相变的广泛研究表明，诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。
The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''—and therefore plausible as a source of natural complexity—rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.
The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous—and therefore plausible as a source of natural complexity—rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.
自组织临界性这个术语最早由 Bak，Tang 和 Wiesenfeld 在1987年的论文中提出，这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂定律) ，这种方式可以与临界点现象联系起来。然而，关键的是，这篇论文强调，观察到的复杂性是以一种强有力的方式出现的，并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变，而不会影响关键行为的出现: 因此，自组织临界性。因此，BTW 论文的关键结果是发现了一种机制，通过这种机制，从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣，产生了一些在科学文献中被引用最多的论文。
Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]].
Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors.
由于 BTW 将他们的模型比喻为一个“沙堆” ，在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ，所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩，其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。
Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a>
Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a>
早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学，试图通过分析证明模型的性质(包括计算临界指数，参见 tang1988a
{{cite journal
{{cite journal
{引用期刊
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]
| author = Tang, C. and Bak, P.
作者 Tang，c. and Bak，p。
| year = 1988
| year = 1988
1988年
| title = Critical exponents and scaling relations for self-organized critical phenomena
| title = Critical exponents and scaling relations for self-organized critical phenomena
自组织临界现象的临界指数和标度关系
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 60
| volume = 60
第60卷
| issue = 23
| issue = 23
第23期
| pages = 2347–2350
| pages = 2347–2350
2347-- 2350
| doi = 10.1103/PhysRevLett.60.2347
| doi = 10.1103/PhysRevLett.60.2347
10.1103 / physrvlett. 60.2347
| bibcode= 1988PhRvL..60.2347T
| bibcode= 1988PhRvL..60.2347T
1988 / phrvl. 60.2347 t
| pmid=10038328
| pmid=10038328
10038328
}}
}}
}}
</ref><ref name=Tang1988b>
</ref><ref name=Tang1988b>
/ ref / name tang1988b
{{cite journal
{{cite journal
{引用期刊
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]
| author = Tang, C. and Bak, P.
作者 Tang，c. and Bak，p。
| year = 1988
| year = 1988
1988年
| title = Mean field theory of self-organized critical phenomena
| title = Mean field theory of self-organized critical phenomena
自组织临界现象的平均场理论
| journal = [[Journal of Statistical Physics]]
| journal = Journal of Statistical Physics
统计物理学杂志
| volume = 51
| volume = 51
第51卷
| issue = 5–6
| issue = 5–6
第5-6期
| pages = 797–802
| pages = 797–802
797802页
| doi = 10.1007/BF01014884
| doi = 10.1007/BF01014884
10.1007 / BF01014884
| bibcode= 1988JSP....51..797T
| bibcode= 1988JSP....51..797T
1988JSP... 51. . 797 t
| url = https://zenodo.org/record/1232502
| url = https://zenodo.org/record/1232502
Https://zenodo.org/record/1232502
| type = Submitted manuscript
| type = Submitted manuscript
| 打印提交的手稿
}}
}}
}}
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.
/ ref) ，以及研究出现 SOC 的必要条件。后一项研究的一个重要问题是，在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的，但有一些保留意见，因为一些交换动态(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看，有待解决的关键理论问题包括 SOC 行为可能的普适性类的计算，以及是否有可能推导出一个确定任意算法是否显示 SOC 的一般规则的问题。
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85>
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85>
除了这些大部分基于实验室的方法，许多其他的研究都集中在大规模的自然或社会系统上，这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ，但 SOC 已经成为解释一些自然现象的强有力的候选者，包括: 地震(早在 SOC 被发现之前，地震就被认为是尺度不变行为的来源，例如描述地震大小统计分布的古腾堡-里克特定律，以及描述余震频率的描述余震的 Omori 定律，命名为 turcottesmalleysolla85
{{cite journal
{{cite journal
{引用期刊
|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985
|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985
1 Turcotte，D.l. | author2 Smalley，r. f. ，jr. | author3 Solla，s. a.1985年
| title = Collapse of loaded fractal trees
| title = Collapse of loaded fractal trees
负载分形树的崩溃
| journal = Nature
| journal = Nature
自然》杂志
| doi= 10.1038/313671a0
| doi= 10.1038/313671a0
10.1038 / 313671a0
| volume = 313
| volume = 313
第313卷
| issue = 6004
| issue = 6004
第6004期
| pages = 671–672|bibcode = 1985Natur.313..671T
| pages = 671–672|bibcode = 1985Natur.313..671T
| 第671-672页 | bibcode 1985 / natur. 313. . 671 t
}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012>
}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012>
太阳耀斑; 经济系统的波动，比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012
{{cite journal
{{cite journal
{引用期刊
| pmid = 22815496
| pmid = 22815496
22815496
|date=Jul 2012
|date=Jul 2012
2012年7月
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks
1 Poil，SS | author2 Hardstone，r | author3 mansveder，HD | author4 Linkenkaer-Hansen，k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中
| volume = 32
| volume = 32
第32卷
| issue = 29
| issue = 29
第29期
| pages = 9817–23
| pages = 9817–23
第9817-23页
| doi = 10.1523/JNEUROSCI.5990-11.2012
| doi = 10.1523/JNEUROSCI.5990-11.2012
| doi 10.1523 / jneurosci. 5990-11.2012
| journal = Journal of Neuroscience
| journal = Journal of Neuroscience
神经科学杂志
| pmc=3553543
| pmc=3553543
3553543
}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.
}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.
{} / ref 1 / f 噪声在电生理信号的振幅，以及生物进化(其中 SOC 已被调用，例如，作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对土壤有机碳的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ，也包括广泛的数据分析，以确定是否存在和 / 或具有自然定标法的特点。
In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018>
In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018>
此外，SOC 已经应用于计算算法。最近，人们发现来自 SOC 过程的雪崩，如 BTW 模型，在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018
{{cite journal
{{cite journal
{引用期刊
| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]
| author = Hoffmann, H. and Payton, D. W.
作者: 霍夫曼 h. 和佩顿 d. w。
| year = 2018
| year = 2018
2018年
| title = Optimization by Self-Organized Criticality
| title = Optimization by Self-Organized Criticality
最佳化作者: 自组织临界性
| journal = [[Scientific Reports]]
| journal = Scientific Reports
科学报告
| volume = 8
| volume = 8
第八卷
| issue = 1
| issue = 1
第一期
| pages = 2358
| pages = 2358
2358页
| doi=10.1038/s41598-018-20275-7
| doi=10.1038/s41598-018-20275-7
10.1038 / s41598-018-20275-7
| pmid = 29402956
| pmid = 29402956
29402956
| pmc = 5799203
| pmc = 5799203
5799203
| bibcode = 2018NatSR...8.2358H
| bibcode = 2018NatSR...8.2358H
| bibcode 2018NatSR... 8.2358 h
}}</ref>
}}</ref>
{} / ref
An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].
An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.
图着色就是这种最佳化问题的一个例子。Soc 过程显然有助于优化陷入局部最优，而无需使用任何退火方案，正如以前的极值优化工作所建议的。
The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>
The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>
无标度网络最近引起的兴奋为 SOC 相关研究提出了一些有趣的新问题: 许多不同的 SOC 模型已经被证明是作为一种涌现现象产生这样的网络，而不是网络研究人员提出的更简单的模型，其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性，但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007
{{cite journal
{{cite journal
{引用期刊
| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]
| author = Moret, M. A. and Zebende, G.
作者: Moret，M.a. and Zebende，g。
| year = 2007
| year = 2007
2007年
| title = Amino acid hydrophobicity and accessible surface area
| title = Amino acid hydrophobicity and accessible surface area
氨基酸疏水性和可达表面积
| journal = [[Phys. Rev. E]]
| journal = Phys. Rev. E
体育杂志。牧师。E
| volume = 75
| volume = 75
第75卷
| issue = 1
| issue = 1
第一期
| pages = 011920
| pages = 011920
011920页
| doi=10.1103/PhysRevE.75.011920
| doi=10.1103/PhysRevE.75.011920
10.1103 / physarve. 75.011920
| pmid = 17358197
| pmid = 17358197
17358197
| bibcode = 2007PhRvE..75a1920M
| bibcode = 2007PhRvE..75a1920M
2007 / phrve. . 75 / a1920M
}}</ref>
}}</ref>
{} / ref
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014>
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014>
这些研究量化了蛋白质的微分几何，并解决了许多关于生物复杂性出现的进化之谜
{{cite journal
{{cite journal
{引用期刊
| author = Phillips, J. C.
| author = Phillips, J. C.
作者: 菲利普斯。
| year = 2014
| year = 2014
2014年
| title = Fractals and self-organized criticality in proteins
| title = Fractals and self-organized criticality in proteins
标题蛋白质中的分形和自组织临界性
| journal = Physica A
| journal = Physica A
物理学杂志 a
| volume = 415
| volume = 415
第415卷
| pages = 440–448
| pages = 440–448
第440-448页
| doi=10.1016/j.physa.2014.08.034
| doi=10.1016/j.physa.2014.08.034
| doi 10.1016 / j.physa. 2014.08.034
| bibcode = 2014PhyA..415..440P
| bibcode = 2014PhyA..415..440P
| bibcode 2014PhyA. . 415. . 440 p
| author-link = J. C. Phillips
| author-link = J. C. Phillips
作者链接 J.c. 菲利普斯
}}</ref>
}}</ref>
{} / ref
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,
尽管 SOC 假说引起了相当大的兴趣和研究成果，但是关于其抽象数学形式的机制仍然没有普遍的一致性。和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989>
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989>
有人认为，这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声
{{cite journal
{{cite journal
{引用期刊
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.
作者 Jensen，h. j. ，Christensen，k. and fogeby，h. c。
| year = 1989
| year = 1989
1989年
| title = 1/f noise, distribution of lifetimes, and a pile of sand
| title = 1/f noise, distribution of lifetimes, and a pile of sand
标题1 / f 噪音，寿命分布，和一堆沙子
| journal = [[Phys. Rev. B]]
| journal = Phys. Rev. B
体育杂志。牧师。B
| volume = 40
| volume = 40
第40卷
| issue = 10
| issue = 10
第10期
| pages = 7425–7427
| pages = 7425–7427
第7425-7427页
| doi=10.1103/physrevb.40.7425
| doi=10.1103/physrevb.40.7425
10.1103 / physirevb. 40.7425
| pmid = 9991162
| pmid = 9991162
9991162
|bibcode = 1989PhRvB..40.7425J }}
|bibcode = 1989PhRvB..40.7425J }}
1989 / phrvb. 40.7425 j }
</ref>
</ref>
/ 参考
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models
这种说法是基于未经测试的比例假设，更严格的分析表明沙堆模型
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005>
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005>
一般产生1 / f sup a / sup 光谱，其值为2。参考名称 laurson2005
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref>
</ref>
/ 参考
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999>
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999>
其他模拟模型后来被提出，可以产生真正的1 / f 噪声，参考名称 maslov1999
{{cite journal
{{cite journal
{引用期刊
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]
| author = Maslov, S., Tang, C. and Zhang, Y. - C.
作者 Maslov，s. ，Tang，c. and Zhang，y。- c.
| year = 1999
| year = 1999
1999年
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音
| journal = [[Phys. Rev. Lett.]]
| journal = Phys. Rev. Lett.
体育杂志。牧师。莱特。
| volume = 83
| volume = 83
第83卷
| issue = 12
| issue = 12
第12期
| pages = 2449–2452
| pages = 2449–2452
2449-2452页
| doi=10.1103/physrevlett.83.2449
| doi=10.1103/physrevlett.83.2449
10.1103 / physrvlett. 83.2449
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996>
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996>
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996
{{cite journal
{{cite journal
{引用期刊
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P
| year = 1996
| year = 1996
1996年
| title = Avalanche dynamics in a pile of rice
| title = Avalanche dynamics in a pile of rice
| 题目: 大米堆中的雪崩动力学
| journal = [[Nature (journal)|Nature]]
| journal = Nature
自然》杂志
| volume = 379
| volume = 379
第379卷
| issue = 6560
| issue = 6560
第6560期
| pages = 49–52
| pages = 49–52
第49-52页
| doi =10.1038/379049a0
| doi =10.1038/379049a0
10.1038 / 379049a0
| bibcode= 1996Natur.379...49F}}
| bibcode= 1996Natur.379...49F}}
1996 / natur. 379... 49F }
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003>
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003>
除了上面提到的非保守理论模型之外，其他关于 SOC 的理论模型都是基于信息论，例如 dewar2003
{{cite journal
{{cite journal
{引用期刊
| author = Dewar, R.
| author = Dewar, R.
作者杜瓦，r。
| year = 2003
| year = 2003
2003年
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释
| journal =J. Phys. A: Math. Gen.
| journal =J. Phys. A: Math. Gen.
| j 杂志。女名女子名。答: 数学。将军。
| volume = 36
| volume = 36
第36卷
| pages =631–641
| pages =631–641
631-- 641
| pmid =
| pmid =
我不会让你失望的
| doi = 10.1088/0305-4470/36/3/303
| doi = 10.1088/0305-4470/36/3/303
10.1088 / 0305-4470 / 36 / 3 / 303
| issue = 3
| issue = 3
第三期
| pmc =
| pmc =
我会的，我会的，我会的
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar
}}</ref>,
}}</ref>,
} / ref,
[[mean field theory]]<ref name=Vespignani1998>
mean field theory<ref name=Vespignani1998>
平均场理论参考名称 vespignani1998
{{cite journal
{{cite journal
{引用期刊
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]
| author = Vespignani, A., and Zapperi, S.
作者 Vespignani，a，和 Zapperi，s。
| year = 1998
| year = 1998
1998年
| title = How self-organized criticality works: a unified mean-field picture
| title = How self-organized criticality works: a unified mean-field picture
标题自组织临界性如何工作: 一个统一的平均场图片
| journal =Phys. Rev. E
| journal =Phys. Rev. E
体育杂志。牧师。E
| volume = 57
| volume = 57
第57卷
| pages =6345–6362
| pages =6345–6362
6345-6362页
| pmid =
| pmid =
我不会让你失望的
| doi = 10.1103/physreve.57.6345
| doi = 10.1103/physreve.57.6345
10.1103 / physorve. 57.6345
| issue = 6
| issue = 6
第六期
| pmc =
| pmc =
我会的，我会的，我会的
| bibcode = 1998PhRvE..57.6345V
| bibcode = 1998PhRvE..57.6345V
| bibcode 1998PhRvE. . 57.6345 v
| arxiv = cond-mat/9709192
| arxiv = cond-mat/9709192
| arxiv = cond-mat/9709192
| hdl = 2047/d20002173
| hdl = 2047/d20002173
2047 / d20002173
}}</ref>,
}}</ref>,
} / ref,
the [[convergence of random variables]]<ref name=Kendal2015>
the convergence of random variables<ref name=Kendal2015>
随机变量的收敛裁判名称 kendal 2015
{{cite journal
{{cite journal
{引用期刊
| author = Kendal, WS
| author = Kendal, WS
作者 Kendal，WS
| year = 2015
| year = 2015
2015年
| title = Self-organized criticality attributed to a central limit-like convergence effect
| title = Self-organized criticality attributed to a central limit-like convergence effect
| 标题自组织临界性归因于类似中心极限的聚合效应
| journal =Physica A
| journal =Physica A
物理学杂志 a
| volume = 421
| volume = 421
第421卷
| pages =141–150
| pages =141–150
141-- 150页
| pmid =
| pmid =
我不会让你失望的
| doi = 10.1016/j.physa.2014.11.035
| doi = 10.1016/j.physa.2014.11.035
| doi 10.1016 / j.physa. 2014.11.035
| issue =
| issue =
发行
| pmc =
| pmc =
我会的，我会的，我会的
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal
}}</ref>,
}}</ref>,
} / ref,
and cluster formation.<ref name=Hoffmann2018b>
and cluster formation.<ref name=Hoffmann2018b>
和簇的形成。参考名称 hoffmann2018b
{{cite journal
{{cite journal
{引用期刊
| author = Hoffmann, H.
| author = Hoffmann, H.
作者: 霍夫曼。
| year = 2018
| year = 2018
2018年
| title = Impact of Network Topology on Self-Organized Criticality
| title = Impact of Network Topology on Self-Organized Criticality
网络拓扑对自组织临界性的影响
| journal = Phys. Rev. E
| journal = Phys. Rev. E
体育杂志。牧师。E
| volume = 97
| volume = 97
第97卷
| pages =022313
| pages =022313
022313页
| pmid = 29548239
| pmid = 29548239
29548239
| doi = 10.1103/PhysRevE.97.022313
| doi = 10.1103/PhysRevE.97.022313
10.1103 / physarve. 97.022313
| issue = 2
| issue = 2
第二期
| pmc =
| pmc =
我会的，我会的，我会的
| bibcode =2018PhRvE..97b2313H
| bibcode =2018PhRvE..97b2313H
2018 / phrve. . 97 / b2313H
| author-link = Heiko Hoffmann
| author-link = Heiko Hoffmann
作者: 海科 · 霍夫曼
| doi-access = free
| doi-access = free
免费访问
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref>
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.
{} / ref 一个自组织临界的连续模型是通过使用热带几何来提出的。
== Examples of self-organized critical dynamics ==
== Examples of self-organized critical dynamics ==
自组织临界动力学的例子
In chronological order of development:
In chronological order of development:
按发展时间顺序排列:
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]
* [[Forest-fire model]]
* [[Olami–Feder–Christensen model]]
* [[Bak–Sneppen model]]
== See also ==
== See also ==
参见
* [[Pink noise|1/f noise]]
* [[Complex system]]s
* [[Critical brain hypothesis]]
* [[Critical exponents]]
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.
* [[Fractal]]s
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.
* [[Power law]]s
* [[Red Queen hypothesis]]
* [[Scale invariance]]
* [[Self-organization]]
* [[Self-organized criticality control]]
==References==
==References==
参考资料
<references/>
== Further reading ==
== Further reading ==
进一步阅读
* {{cite journal
| author = Adami, C.
| author = Adami, C.
作者: 阿达米。
| year = 1995
| year = 1995
1995年
| title = Self-organized criticality in living systems
| title = Self-organized criticality in living systems
| 生命系统中的自组织临界性
| journal = [[Physics Letters A]]
| journal = Physics Letters A
物理学快报
| volume = 203
| volume = 203
第203卷
| issue = 1
| issue = 1
第一期
| pages = 29–32
| pages = 29–32
29-- 32页
| doi = 10.1016/0375-9601(95)00372-A
| doi = 10.1016/0375-9601(95)00372-A
| doi 10.1016 / 0375-9601(95)00372-A
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001
| citeseerx = 10.1.1.456.9543
| citeseerx = 10.1.1.456.9543
10.1.1.456.9543
| author-link = Adami, C
| author-link = Adami, C
| 作者链接阿达米，c
}}
}}
}}
* {{cite book
| author = Bak, P.
| author = Bak, P.
作者 Bak，p。
| year = 1996
| year = 1996
1996年
| title = How Nature Works: The Science of Self-Organized Criticality
| title = How Nature Works: The Science of Self-Organized Criticality
自然如何运作: 自组织临界性的科学
| publisher = Copernicus
| publisher = Copernicus
出版商哥白尼
| location = New York
| location = New York
| 地点: 纽约
| isbn = 978-0-387-94791-4
| isbn = 978-0-387-94791-4
[国际标准图书编号978-0-387-94791-4]
| author-link = Per Bak
| author-link = Per Bak
| 作者链接 Per Bak
}}
}}
}}
* {{cite journal
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]
| author = Bak, P. and Paczuski, M.
作者 Bak，p. and Paczuski，m。
| year = 1995
| year = 1995
1995年
| title = Complexity, contingency, and criticality
| title = Complexity, contingency, and criticality
| 标题复杂性、偶然性和临界性
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]
| journal = Proceedings of the National Academy of Sciences of the USA
美国美国国家科学院院刊杂志
| volume = 92
| volume = 92
第92卷
| pages = 6689–6696
| pages = 6689–6696
6689-- 6696
| url = http://pnas.org/cgi/content/abstract/92/15/6689
| url = http://pnas.org/cgi/content/abstract/92/15/6689
Http://pnas.org/cgi/content/abstract/92/15/6689
| doi = 10.1073/pnas.92.15.6689
| doi = 10.1073/pnas.92.15.6689
10.1073 / pnas. 92.15.6689
| pmid = 11607561
| pmid = 11607561
11607561
| issue = 15
| issue = 15
第15期
| pmc = 41396
| pmc = 41396
41396
|bibcode = 1995PNAS...92.6689B }}
|bibcode = 1995PNAS...92.6689B }}
92.6689 b }
* {{cite journal
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]
| author = Bak, P. and Sneppen, K.
作者 Bak，p. and Sneppen，k。
| year = 1993
| year = 1993
1993年
| title = Punctuated equilibrium and criticality in a simple model of evolution
| title = Punctuated equilibrium and criticality in a simple model of evolution
| 简单演化模型中的间断平衡和临界性
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 71
| volume = 71
第71卷
| issue = 24
| issue = 24
第24期
| pages = 4083–4086
| pages = 4083–4086
4083-- 4086
| doi = 10.1103/PhysRevLett.71.4083
| doi = 10.1103/PhysRevLett.71.4083
10.1103 / physrvlett. 71.4083
| pmid=10055149
| pmid=10055149
10055149
| bibcode=1993PhRvL..71.4083B}}
| bibcode=1993PhRvL..71.4083B}}
1993 phrvl. . 71.4083 b }
* {{cite journal
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| author = Bak, P., Tang, C. and Wiesenfeld, K.
作者 Bak，p. ，Tang，c. and Wiesenfeld，k。
| year = 1987
| year = 1987
1987年
| title = Self-organized criticality: an explanation of <math>1/f</math> noise
| title = Self-organized criticality: an explanation of <math>1/f</math> noise
| 题目自组织临界性: 数学噪音的解释
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 59
| volume = 59
第59卷
| issue = 4
| issue = 4
第四期
| pages = 381–384
| pages = 381–384
381-- 384
| doi = 10.1103/PhysRevLett.59.381
| doi = 10.1103/PhysRevLett.59.381
10.1103 / physrvlett. 59.381
| pmid = 10035754
| pmid = 10035754
10035754
| bibcode=1987PhRvL..59..381B}}
| bibcode=1987PhRvL..59..381B}}
1987 / phrvl. . 59. . 381 b }
* {{cite journal
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| author = Bak, P., Tang, C. and Wiesenfeld, K.
作者 Bak，p. ，Tang，c. and Wiesenfeld，k。
| year = 1988
| year = 1988
1988年
| title = Self-organized criticality
| title = Self-organized criticality
标题自组织临界性
| journal = [[Physical Review A]]
| journal = Physical Review A
物理评论 a 期刊
| volume = 38
| volume = 38
第38卷
| issue = 1
| issue = 1
第一期
| pages = 364–374
| pages = 364–374
364-- 374
| doi = 10.1103/PhysRevA.38.364
| doi = 10.1103/PhysRevA.38.364
10.1103 / PhysRevA. 38.364
| pmid = 9900174
| pmid = 9900174
9900174
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。
* {{cite book
| author = Buchanan, M.
| author = Buchanan, M.
作者: 布坎南。
| year = 2000
| year = 2000
2000年
| title = Ubiquity
| title = Ubiquity
标题: Ubiquity
| publisher = Weidenfeld & Nicolson
| publisher = Weidenfeld & Nicolson
| publisher = Weidenfeld & Nicolson
| location = London
| location = London
地点: 伦敦
| isbn = 978-0-7538-1297-6
| isbn = 978-0-7538-1297-6
[国际标准图书编号978-0-7538-1297-6]
| author-link = Mark Buchanan
| author-link = Mark Buchanan
马克 · 布坎南
}}
}}
}}
* {{cite book
| author = Jensen, H. J.
| author = Jensen, H. J.
作者 Jensen，h. j。
| year = 1998
| year = 1998
1998年
| title = Self-Organized Criticality
| title = Self-Organized Criticality
标题自组织临界性
| publisher = [[Cambridge University Press]]
| publisher = Cambridge University Press
出版商剑桥大学出版社
| location = Cambridge
| location = Cambridge
| 地点: 剑桥
| isbn = 978-0-521-48371-1
| isbn = 978-0-521-48371-1
[国际标准图书编号978-0-521-48371-1]
| author-link = Henrik Jeldtoft Jensen
| author-link = Henrik Jeldtoft Jensen
作者: 亨里克 · 耶尔德托夫特 · 詹森
}}
}}
}}
* {{cite journal
| author = Katz, J. I.
| author = Katz, J. I.
作者 Katz，j. i。
| year = 1986
| year = 1986
1986年
| title = A model of propagating brittle failure in heterogeneous media
| title = A model of propagating brittle failure in heterogeneous media
在非均匀介质中传播脆性破坏的模型
| journal = Journal of Geophysical Research
| journal = Journal of Geophysical Research
地球物理研究期刊
| bibcode = 1986JGR....9110412K
| bibcode = 1986JGR....9110412K
| bibcode 1986JGR... 9110412K
| doi = 10.1029/JB091iB10p10412
| doi = 10.1029/JB091iB10p10412
| doi 10.1029 / JB091iB10p10412
| volume = 91
| volume = 91
第91卷
| issue = B10
| issue = B10
第10期
| pages = 10412
| pages = 10412
10412页
}}
}}
}}
* {{cite journal
| author = Kron, T./Grund, T.
| author = Kron, T./Grund, T.
作者: Kron t. / Grund t。
| year = 2009
| year = 2009
2009年
| title = Society as a Selforganized Critical System
| title = Society as a Selforganized Critical System
作为一个自组织的批判系统的社会
| journal = Cybernetics and Human Knowing
| journal = Cybernetics and Human Knowing
控制论与人类认知
| volume = 16
| volume = 16
第16卷
| pages = 65–82
| pages = 65–82
第65-82页
}}
}}
}}
* {{Cite book
| author = Paczuski, M.
| author = Paczuski, M.
作者: 帕祖斯基。
| year = 2005
| year = 2005
2005年
| title = Networks as renormalized models for emergent behavior in physical systems
| title = Networks as renormalized models for emergent behavior in physical systems
作为物理系统中突发行为的重整化模型的网络
| journal = Complexity
| journal = Complexity
杂志复杂性
| pages = 363–374
| pages = 363–374
第363-374页
| arxiv = physics/0502028
| arxiv = physics/0502028
| arxiv physics / 0502028
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042
| series = The Science and Culture Series – Physics
| series = The Science and Culture Series – Physics
| 科学与文化系列-物理学
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886
| author-link = Maya Paczuski
| author-link = Maya Paczuski
| 作者链接 Maya Paczuski
}}
}}
}}
* {{cite book
| author = Turcotte, D. L.
| author = Turcotte, D. L.
作者: Turcotte，D.l。
| year = 1997
| year = 1997
1997年
| title = Fractals and Chaos in Geology and Geophysics
| title = Fractals and Chaos in Geology and Geophysics
地质学与地球物理学中的分形与混沌
| publisher = [[Cambridge University Press]]
| publisher = Cambridge University Press
出版商剑桥大学出版社
| location = Cambridge
| location = Cambridge
| 地点: 剑桥
| isbn = 978-0-521-56733-6
| isbn = 978-0-521-56733-6
[国际标准图书馆编号978-0-521-56733-6]
| author-link = Donald L. Turcotte
| author-link = Donald L. Turcotte
作者: Donald l. Turcotte
}}
}}
}}
* {{cite journal
| author = Turcotte, D. L.
| author = Turcotte, D. L.
作者: Turcotte，D.l。
| year = 1999
| year = 1999
1999年
| title = Self-organized criticality
| title = Self-organized criticality
标题自组织临界性
| journal = [[Reports on Progress in Physics]]
| journal = Reports on Progress in Physics
物理学进展报告
| volume = 62
| volume = 62
第62卷
| issue = 10
| issue = 10
第10期
| pages = 1377–1429
| pages = 1377–1429
13771429页
| doi = 10.1088/0034-4885/62/10/201
| doi = 10.1088/0034-4885/62/10/201
10.1088 / 0034-4885 / 62 / 10 / 201
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte
}}
}}
}}
* {{cite journal
| author = Md. Nurujjaman/A. N. Sekar Iyengar
| author = Md. Nurujjaman/A. N. Sekar Iyengar
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar
| year = 2007
| year = 2007
2007年
| title = Realization of {SOC} behavior in a dc glow discharge plasma
| title = Realization of {SOC} behavior in a dc glow discharge plasma
直流辉光放电等离子体{ SOC }行为的实现
| journal = [[Physics Letters A]]
| journal = Physics Letters A
物理学快报
| volume = 360
| volume = 360
第360卷
| issue = 6
| issue = 6
第六期
| pages = 717–721
| pages = 717–721
717-- 721页
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar
| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar
}}
}}
}}
*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]
[[Category:Critical phenomena]]
Category:Critical phenomena
范畴: 关键现象
[[Category:Applied and interdisciplinary physics]]
Category:Applied and interdisciplinary physics
类别: 应用和跨学科物理学
[[Category:Chaos theory]]
Category:Chaos theory
范畴: 混沌理论
[[Category:Self-organization]]
Category:Self-organization
类别: 自我组织
<noinclude>
<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude>
[[Category:待整理页面]]
In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.
在物理学中，自组织临界性是动力系统的一种特性，动力系统有一个临界点作为吸引子。它们的宏观行为因此显示了相变临界点的空间或时间尺度不变特性，但不需要调整控制参数到一个精确的值，因为系统有效地调整自己，因为它进化到临界状态。
The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987>
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987>
这个概念是由 Per Bak，Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的
{{cite journal
{{cite journal
{引用期刊
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| author = Bak, P., Tang, C. and Wiesenfeld, K.
作者 Bak，p. ，Tang，c. and Wiesenfeld，k。
| year = 1987
| year = 1987
1987年
| title = Self-organized criticality: an explanation of 1/''f'' noise
| title = Self-organized criticality: an explanation of 1/f noise
自组织临界性: 1 / f 噪音的解释
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 59
| volume = 59
第59卷
| issue = 4
| issue = 4
第四期
| pages = 381–384
| pages = 381–384
381-- 384
| doi = 10.1103/PhysRevLett.59.381
| doi = 10.1103/PhysRevLett.59.381
10.1103 / physrvlett. 59.381
| pmid = 10035754
| pmid = 10035754
10035754
| bibcode=1987PhRvL..59..381B
| bibcode=1987PhRvL..59..381B
| bibcode 1987PhRvL. . 59. . 381 b
}}
}}
}}
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref>
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref>
论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考
published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995>
published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995>
1987年发表在《物理评论快报》上，被认为是复杂性的机制之一
{{cite journal
{{cite journal
{引用期刊
| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]
| author = Bak, P., and Paczuski, M.
作者 Bak，p，and Paczuski，m。
| year = 1995
| year = 1995
1995年
| title = Complexity, contingency, and criticality
| title = Complexity, contingency, and criticality
| 标题复杂性、偶然性和临界性
| journal =Proc Natl Acad Sci U S A
| journal =Proc Natl Acad Sci U S A
美国科学促进协会
| volume = 92
| volume = 92
第92卷
| pages = 6689–6696
| pages = 6689–6696
6689-- 6696
| pmid = 11607561
| pmid = 11607561
11607561
| doi = 10.1073/pnas.92.15.6689
| doi = 10.1073/pnas.92.15.6689
10.1073 / pnas. 92.15.6689
| issue = 15
| issue = 15
第15期
| pmc = 41396
| pmc = 41396
41396
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85>
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85>
| bibcode 1995PNAS... 92.6689 b } / ref 在自然界中出现。它的概念已经被应用于各个领域，比如地球物理学，参考名称 smalleyturcottesolla85
{{cite journal
{{cite journal
{引用期刊
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985
1 Smalley，r. f. ，jr. | author2 Turcotte，d. l. | author3 Solla，s. a.1985年
| title = A renormalization group approach to the stick-slip behavior of faults
| title = A renormalization group approach to the stick-slip behavior of faults
| 题目: 断层粘滑行为的重整化群方法
| journal = Journal of Geophysical Research
| journal = Journal of Geophysical Research
地球物理研究期刊
| bibcode = 1985JGR....90.1894S
| bibcode = 1985JGR....90.1894S
1985JGR... 90.1894 s
| doi = 10.1029/JB090iB02p01894
| doi = 10.1029/JB090iB02p01894
| doi 10.1029 / JB090iB02p01894
| volume = 90
| volume = 90
第90卷
| issue = B2
| issue = B2
| 第二期
| pages = 1894
| pages = 1894
1894页
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001>
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001>
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学，进化生物学和生态学，生物启发计算和优化(数学) ，经济学，量子引力，社会学，太阳物理学，等离子物理学，神经生物学参考名称 linkenkaerhansen2001
{{cite journal
{{cite journal
{引用期刊
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
人类大脑振荡中的长程时间相关性和标度行为
| journal = J. Neurosci.
| journal = J. Neurosci.
作者: j. Neurosci。
| volume = 21
| volume = 21
第21卷
| pages = 1370–1377
| pages = 1370–1377
1370-- 1377
| pmid = 11160408
| pmid = 11160408
11160408
| issue = 4
| issue = 4
第四期
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003>
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003>
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003
{{cite journal
{{cite journal
{引用期刊
|author1=J. M. Beggs |author2=D. Plenz
|author1=J. M. Beggs |author2=D. Plenz
1 j.2 d.Plenz
|lastauthoramp=yes | year = 2006
|lastauthoramp=yes | year = 2006
2006年
| title = Neuronal Avalanches in Neocortical Circuits
| title = Neuronal Avalanches in Neocortical Circuits
新皮层神经回路中的神经雪崩
| journal = J. Neurosci.
| journal = J. Neurosci.
作者: j. Neurosci。
| volume = 23
| volume = 23
第23卷
|issue=35
|issue=35
第35期
|pages=11167–77
|pages=11167–77
第11167-77页
|doi=10.1523/JNEUROSCI.23-35-11167.2003
|doi=10.1523/JNEUROSCI.23-35-11167.2003
10.1523 / jneurosci. 23-35-11167.2003
|pmid=14657176
|pmid=14657176
14657176
|pmc=6741045
|pmc=6741045
6741045
}}</ref><ref name=Chialvo2004>
}}</ref><ref name=Chialvo2004>
} / ref ref name chialvo2004
{{cite journal
{{cite journal
{引用期刊
| author =Chialvo, D. R.
| author =Chialvo, D. R.
作者 Chialvo，d. r。
| year = 2004
| year = 2004
2004年
| title = Critical brain networks
| title = Critical brain networks
关键的大脑网络
| journal = Physica A
| journal = Physica A
物理学杂志 a
| volume = 340
| volume = 340
第340卷
| issue =4
| issue =4
第四期
| pages = 756–765
| pages = 756–765
756-- 765
| doi = 10.1016/j.physa.2004.05.064
| doi = 10.1016/j.physa.2004.05.064
10.1016 / j.physa. 2004.05.064
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo
}}</ref> and others.
}}</ref> and others.
} / ref and others.
SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.
SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.
Soc 是典型的多自由度、强非线性动力学的缓慢驱动非平衡系统。自从 BTW 的原始论文以来，已经确定了许多单独的例子，但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 SOC。
== Overview ==
== Overview ==
概览
Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.
Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.
自组织临界性是20世纪下半叶统计物理学及相关领域的众多重要发现之一，这些发现尤其与研究自然界的复杂性有关。例如，细胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的《生命的游戏》和 Stephen Wolfram 的大量工作---- 清楚地表明，复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内，beno t Mandelbrot 关于分形的大量工作表明，自然界的许多复杂性可以用某些无处不在的数学定律来描述，而在20世纪60年代和70年代对相变的广泛研究表明，诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。
The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''—and therefore plausible as a source of natural complexity—rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.
The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous—and therefore plausible as a source of natural complexity—rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.
自组织临界性这个术语最早由 Bak，Tang 和 Wiesenfeld 在1987年的论文中提出，这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂定律) ，这种方式可以与临界点现象联系起来。然而，关键的是，这篇论文强调，观察到的复杂性是以一种强有力的方式出现的，并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变，而不会影响关键行为的出现: 因此，自组织临界性。因此，BTW 论文的关键结果是发现了一种机制，通过这种机制，从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣，产生了一些在科学文献中被引用最多的论文。
Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]].
Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors.
由于 BTW 将他们的模型比喻为一个“沙堆” ，在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ，所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩，其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。
Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a>
Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a>
早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学，试图通过分析证明模型的性质(包括计算临界指数，参见 tang1988a
{{cite journal
{{cite journal
{引用期刊
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]
| author = Tang, C. and Bak, P.
作者 Tang，c. and Bak，p。
| year = 1988
| year = 1988
1988年
| title = Critical exponents and scaling relations for self-organized critical phenomena
| title = Critical exponents and scaling relations for self-organized critical phenomena
自组织临界现象的临界指数和标度关系
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 60
| volume = 60
第60卷
| issue = 23
| issue = 23
第23期
| pages = 2347–2350
| pages = 2347–2350
2347-- 2350
| doi = 10.1103/PhysRevLett.60.2347
| doi = 10.1103/PhysRevLett.60.2347
10.1103 / physrvlett. 60.2347
| bibcode= 1988PhRvL..60.2347T
| bibcode= 1988PhRvL..60.2347T
1988 / phrvl. 60.2347 t
| pmid=10038328
| pmid=10038328
10038328
}}
}}
}}
</ref><ref name=Tang1988b>
</ref><ref name=Tang1988b>
/ ref / name tang1988b
{{cite journal
{{cite journal
{引用期刊
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]
| author = Tang, C. and Bak, P.
作者 Tang，c. and Bak，p。
| year = 1988
| year = 1988
1988年
| title = Mean field theory of self-organized critical phenomena
| title = Mean field theory of self-organized critical phenomena
自组织临界现象的平均场理论
| journal = [[Journal of Statistical Physics]]
| journal = Journal of Statistical Physics
统计物理学杂志
| volume = 51
| volume = 51
第51卷
| issue = 5–6
| issue = 5–6
第5-6期
| pages = 797–802
| pages = 797–802
797802页
| doi = 10.1007/BF01014884
| doi = 10.1007/BF01014884
10.1007 / BF01014884
| bibcode= 1988JSP....51..797T
| bibcode= 1988JSP....51..797T
1988JSP... 51. . 797 t
| url = https://zenodo.org/record/1232502
| url = https://zenodo.org/record/1232502
Https://zenodo.org/record/1232502
| type = Submitted manuscript
| type = Submitted manuscript
| 打印提交的手稿
}}
}}
}}
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.
/ ref) ，以及研究出现 SOC 的必要条件。后一项研究的一个重要问题是，在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的，但有一些保留意见，因为一些交换动态(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看，有待解决的关键理论问题包括 SOC 行为可能的普适性类的计算，以及是否有可能推导出一个确定任意算法是否显示 SOC 的一般规则的问题。
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85>
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85>
除了这些大部分基于实验室的方法，许多其他的研究都集中在大规模的自然或社会系统上，这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ，但 SOC 已经成为解释一些自然现象的强有力的候选者，包括: 地震(早在 SOC 被发现之前，地震就被认为是尺度不变行为的来源，例如描述地震大小统计分布的古腾堡-里克特定律，以及描述余震频率的描述余震的 Omori 定律，命名为 turcottesmalleysolla85
{{cite journal
{{cite journal
{引用期刊
|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985
|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985
1 Turcotte，D.l. | author2 Smalley，r. f. ，jr. | author3 Solla，s. a.1985年
| title = Collapse of loaded fractal trees
| title = Collapse of loaded fractal trees
负载分形树的崩溃
| journal = Nature
| journal = Nature
自然》杂志
| doi= 10.1038/313671a0
| doi= 10.1038/313671a0
10.1038 / 313671a0
| volume = 313
| volume = 313
第313卷
| issue = 6004
| issue = 6004
第6004期
| pages = 671–672|bibcode = 1985Natur.313..671T
| pages = 671–672|bibcode = 1985Natur.313..671T
| 第671-672页 | bibcode 1985 / natur. 313. . 671 t
}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012>
}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012>
太阳耀斑; 经济系统的波动，比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012
{{cite journal
{{cite journal
{引用期刊
| pmid = 22815496
| pmid = 22815496
22815496
|date=Jul 2012
|date=Jul 2012
2012年7月
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks
1 Poil，SS | author2 Hardstone，r | author3 mansveder，HD | author4 Linkenkaer-Hansen，k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中
| volume = 32
| volume = 32
第32卷
| issue = 29
| issue = 29
第29期
| pages = 9817–23
| pages = 9817–23
第9817-23页
| doi = 10.1523/JNEUROSCI.5990-11.2012
| doi = 10.1523/JNEUROSCI.5990-11.2012
| doi 10.1523 / jneurosci. 5990-11.2012
| journal = Journal of Neuroscience
| journal = Journal of Neuroscience
神经科学杂志
| pmc=3553543
| pmc=3553543
3553543
}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.
}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.
{} / ref 1 / f 噪声在电生理信号的振幅，以及生物进化(其中 SOC 已被调用，例如，作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对土壤有机碳的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ，也包括广泛的数据分析，以确定是否存在和 / 或具有自然定标法的特点。
In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018>
In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018>
此外，SOC 已经应用于计算算法。最近，人们发现来自 SOC 过程的雪崩，如 BTW 模型，在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018
{{cite journal
{{cite journal
{引用期刊
| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]
| author = Hoffmann, H. and Payton, D. W.
作者: 霍夫曼 h. 和佩顿 d. w。
| year = 2018
| year = 2018
2018年
| title = Optimization by Self-Organized Criticality
| title = Optimization by Self-Organized Criticality
最佳化作者: 自组织临界性
| journal = [[Scientific Reports]]
| journal = Scientific Reports
科学报告
| volume = 8
| volume = 8
第八卷
| issue = 1
| issue = 1
第一期
| pages = 2358
| pages = 2358
2358页
| doi=10.1038/s41598-018-20275-7
| doi=10.1038/s41598-018-20275-7
10.1038 / s41598-018-20275-7
| pmid = 29402956
| pmid = 29402956
29402956
| pmc = 5799203
| pmc = 5799203
5799203
| bibcode = 2018NatSR...8.2358H
| bibcode = 2018NatSR...8.2358H
| bibcode 2018NatSR... 8.2358 h
}}</ref>
}}</ref>
{} / ref
An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].
An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.
图着色就是这种最佳化问题的一个例子。Soc 过程显然有助于优化陷入局部最优，而无需使用任何退火方案，正如以前的极值优化工作所建议的。
The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>
The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>
无标度网络最近引起的兴奋为 SOC 相关研究提出了一些有趣的新问题: 许多不同的 SOC 模型已经被证明是作为一种涌现现象产生这样的网络，而不是网络研究人员提出的更简单的模型，其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性，但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007
{{cite journal
{{cite journal
{引用期刊
| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]
| author = Moret, M. A. and Zebende, G.
作者: Moret，M.a. and Zebende，g。
| year = 2007
| year = 2007
2007年
| title = Amino acid hydrophobicity and accessible surface area
| title = Amino acid hydrophobicity and accessible surface area
氨基酸疏水性和可达表面积
| journal = [[Phys. Rev. E]]
| journal = Phys. Rev. E
体育杂志。牧师。E
| volume = 75
| volume = 75
第75卷
| issue = 1
| issue = 1
第一期
| pages = 011920
| pages = 011920
011920页
| doi=10.1103/PhysRevE.75.011920
| doi=10.1103/PhysRevE.75.011920
10.1103 / physarve. 75.011920
| pmid = 17358197
| pmid = 17358197
17358197
| bibcode = 2007PhRvE..75a1920M
| bibcode = 2007PhRvE..75a1920M
2007 / phrve. . 75 / a1920M
}}</ref>
}}</ref>
{} / ref
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014>
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014>
这些研究量化了蛋白质的微分几何，并解决了许多关于生物复杂性出现的进化之谜
{{cite journal
{{cite journal
{引用期刊
| author = Phillips, J. C.
| author = Phillips, J. C.
作者: 菲利普斯。
| year = 2014
| year = 2014
2014年
| title = Fractals and self-organized criticality in proteins
| title = Fractals and self-organized criticality in proteins
标题蛋白质中的分形和自组织临界性
| journal = Physica A
| journal = Physica A
物理学杂志 a
| volume = 415
| volume = 415
第415卷
| pages = 440–448
| pages = 440–448
第440-448页
| doi=10.1016/j.physa.2014.08.034
| doi=10.1016/j.physa.2014.08.034
| doi 10.1016 / j.physa. 2014.08.034
| bibcode = 2014PhyA..415..440P
| bibcode = 2014PhyA..415..440P
| bibcode 2014PhyA. . 415. . 440 p
| author-link = J. C. Phillips
| author-link = J. C. Phillips
作者链接 J.c. 菲利普斯
}}</ref>
}}</ref>
{} / ref
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,
尽管 SOC 假说引起了相当大的兴趣和研究成果，但是关于其抽象数学形式的机制仍然没有普遍的一致性。和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989>
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989>
有人认为，这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声
{{cite journal
{{cite journal
{引用期刊
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.
作者 Jensen，h. j. ，Christensen，k. and fogeby，h. c。
| year = 1989
| year = 1989
1989年
| title = 1/f noise, distribution of lifetimes, and a pile of sand
| title = 1/f noise, distribution of lifetimes, and a pile of sand
标题1 / f 噪音，寿命分布，和一堆沙子
| journal = [[Phys. Rev. B]]
| journal = Phys. Rev. B
体育杂志。牧师。B
| volume = 40
| volume = 40
第40卷
| issue = 10
| issue = 10
第10期
| pages = 7425–7427
| pages = 7425–7427
第7425-7427页
| doi=10.1103/physrevb.40.7425
| doi=10.1103/physrevb.40.7425
10.1103 / physirevb. 40.7425
| pmid = 9991162
| pmid = 9991162
9991162
|bibcode = 1989PhRvB..40.7425J }}
|bibcode = 1989PhRvB..40.7425J }}
1989 / phrvb. 40.7425 j }
</ref>
</ref>
/ 参考
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models
这种说法是基于未经测试的比例假设，更严格的分析表明沙堆模型
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005>
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005>
一般产生1 / f sup a / sup 光谱，其值为2。参考名称 laurson2005
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref>
</ref>
/ 参考
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999>
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999>
其他模拟模型后来被提出，可以产生真正的1 / f 噪声，参考名称 maslov1999
{{cite journal
{{cite journal
{引用期刊
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]
| author = Maslov, S., Tang, C. and Zhang, Y. - C.
作者 Maslov，s. ，Tang，c. and Zhang，y。- c.
| year = 1999
| year = 1999
1999年
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音
| journal = [[Phys. Rev. Lett.]]
| journal = Phys. Rev. Lett.
体育杂志。牧师。莱特。
| volume = 83
| volume = 83
第83卷
| issue = 12
| issue = 12
第12期
| pages = 2449–2452
| pages = 2449–2452
2449-2452页
| doi=10.1103/physrevlett.83.2449
| doi=10.1103/physrevlett.83.2449
10.1103 / physrvlett. 83.2449
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996>
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996>
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996
{{cite journal
{{cite journal
{引用期刊
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P
| year = 1996
| year = 1996
1996年
| title = Avalanche dynamics in a pile of rice
| title = Avalanche dynamics in a pile of rice
| 题目: 大米堆中的雪崩动力学
| journal = [[Nature (journal)|Nature]]
| journal = Nature
自然》杂志
| volume = 379
| volume = 379
第379卷
| issue = 6560
| issue = 6560
第6560期
| pages = 49–52
| pages = 49–52
第49-52页
| doi =10.1038/379049a0
| doi =10.1038/379049a0
10.1038 / 379049a0
| bibcode= 1996Natur.379...49F}}
| bibcode= 1996Natur.379...49F}}
1996 / natur. 379... 49F }
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003>
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003>
除了上面提到的非保守理论模型之外，其他关于 SOC 的理论模型都是基于信息论，例如 dewar2003
{{cite journal
{{cite journal
{引用期刊
| author = Dewar, R.
| author = Dewar, R.
作者杜瓦，r。
| year = 2003
| year = 2003
2003年
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释
| journal =J. Phys. A: Math. Gen.
| journal =J. Phys. A: Math. Gen.
| j 杂志。女名女子名。答: 数学。将军。
| volume = 36
| volume = 36
第36卷
| pages =631–641
| pages =631–641
631-- 641
| pmid =
| pmid =
我不会让你失望的
| doi = 10.1088/0305-4470/36/3/303
| doi = 10.1088/0305-4470/36/3/303
10.1088 / 0305-4470 / 36 / 3 / 303
| issue = 3
| issue = 3
第三期
| pmc =
| pmc =
我会的，我会的，我会的
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar
}}</ref>,
}}</ref>,
} / ref,
[[mean field theory]]<ref name=Vespignani1998>
mean field theory<ref name=Vespignani1998>
平均场理论参考名称 vespignani1998
{{cite journal
{{cite journal
{引用期刊
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]
| author = Vespignani, A., and Zapperi, S.
作者 Vespignani，a，和 Zapperi，s。
| year = 1998
| year = 1998
1998年
| title = How self-organized criticality works: a unified mean-field picture
| title = How self-organized criticality works: a unified mean-field picture
标题自组织临界性如何工作: 一个统一的平均场图片
| journal =Phys. Rev. E
| journal =Phys. Rev. E
体育杂志。牧师。E
| volume = 57
| volume = 57
第57卷
| pages =6345–6362
| pages =6345–6362
6345-6362页
| pmid =
| pmid =
我不会让你失望的
| doi = 10.1103/physreve.57.6345
| doi = 10.1103/physreve.57.6345
10.1103 / physorve. 57.6345
| issue = 6
| issue = 6
第六期
| pmc =
| pmc =
我会的，我会的，我会的
| bibcode = 1998PhRvE..57.6345V
| bibcode = 1998PhRvE..57.6345V
| bibcode 1998PhRvE. . 57.6345 v
| arxiv = cond-mat/9709192
| arxiv = cond-mat/9709192
| arxiv = cond-mat/9709192
| hdl = 2047/d20002173
| hdl = 2047/d20002173
2047 / d20002173
}}</ref>,
}}</ref>,
} / ref,
the [[convergence of random variables]]<ref name=Kendal2015>
the convergence of random variables<ref name=Kendal2015>
随机变量的收敛裁判名称 kendal 2015
{{cite journal
{{cite journal
{引用期刊
| author = Kendal, WS
| author = Kendal, WS
作者 Kendal，WS
| year = 2015
| year = 2015
2015年
| title = Self-organized criticality attributed to a central limit-like convergence effect
| title = Self-organized criticality attributed to a central limit-like convergence effect
| 标题自组织临界性归因于类似中心极限的聚合效应
| journal =Physica A
| journal =Physica A
物理学杂志 a
| volume = 421
| volume = 421
第421卷
| pages =141–150
| pages =141–150
141-- 150页
| pmid =
| pmid =
我不会让你失望的
| doi = 10.1016/j.physa.2014.11.035
| doi = 10.1016/j.physa.2014.11.035
| doi 10.1016 / j.physa. 2014.11.035
| issue =
| issue =
发行
| pmc =
| pmc =
我会的，我会的，我会的
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal
}}</ref>,
}}</ref>,
} / ref,
and cluster formation.<ref name=Hoffmann2018b>
and cluster formation.<ref name=Hoffmann2018b>
和簇的形成。参考名称 hoffmann2018b
{{cite journal
{{cite journal
{引用期刊
| author = Hoffmann, H.
| author = Hoffmann, H.
作者: 霍夫曼。
| year = 2018
| year = 2018
2018年
| title = Impact of Network Topology on Self-Organized Criticality
| title = Impact of Network Topology on Self-Organized Criticality
网络拓扑对自组织临界性的影响
| journal = Phys. Rev. E
| journal = Phys. Rev. E
体育杂志。牧师。E
| volume = 97
| volume = 97
第97卷
| pages =022313
| pages =022313
022313页
| pmid = 29548239
| pmid = 29548239
29548239
| doi = 10.1103/PhysRevE.97.022313
| doi = 10.1103/PhysRevE.97.022313
10.1103 / physarve. 97.022313
| issue = 2
| issue = 2
第二期
| pmc =
| pmc =
我会的，我会的，我会的
| bibcode =2018PhRvE..97b2313H
| bibcode =2018PhRvE..97b2313H
2018 / phrve. . 97 / b2313H
| author-link = Heiko Hoffmann
| author-link = Heiko Hoffmann
作者: 海科 · 霍夫曼
| doi-access = free
| doi-access = free
免费访问
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref>
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.
{} / ref 一个自组织临界的连续模型是通过使用热带几何来提出的。
== Examples of self-organized critical dynamics ==
== Examples of self-organized critical dynamics ==
自组织临界动力学的例子
In chronological order of development:
In chronological order of development:
按发展时间顺序排列:
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]
* [[Forest-fire model]]
* [[Olami–Feder–Christensen model]]
* [[Bak–Sneppen model]]
== See also ==
== See also ==
参见
* [[Pink noise|1/f noise]]
* [[Complex system]]s
* [[Critical brain hypothesis]]
* [[Critical exponents]]
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.
* [[Fractal]]s
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.
* [[Power law]]s
* [[Red Queen hypothesis]]
* [[Scale invariance]]
* [[Self-organization]]
* [[Self-organized criticality control]]
==References==
==References==
参考资料
<references/>
== Further reading ==
== Further reading ==
进一步阅读
* {{cite journal
| author = Adami, C.
| author = Adami, C.
作者: 阿达米。
| year = 1995
| year = 1995
1995年
| title = Self-organized criticality in living systems
| title = Self-organized criticality in living systems
| 生命系统中的自组织临界性
| journal = [[Physics Letters A]]
| journal = Physics Letters A
物理学快报
| volume = 203
| volume = 203
第203卷
| issue = 1
| issue = 1
第一期
| pages = 29–32
| pages = 29–32
29-- 32页
| doi = 10.1016/0375-9601(95)00372-A
| doi = 10.1016/0375-9601(95)00372-A
| doi 10.1016 / 0375-9601(95)00372-A
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001
| citeseerx = 10.1.1.456.9543
| citeseerx = 10.1.1.456.9543
10.1.1.456.9543
| author-link = Adami, C
| author-link = Adami, C
| 作者链接阿达米，c
}}
}}
}}
* {{cite book
| author = Bak, P.
| author = Bak, P.
作者 Bak，p。
| year = 1996
| year = 1996
1996年
| title = How Nature Works: The Science of Self-Organized Criticality
| title = How Nature Works: The Science of Self-Organized Criticality
自然如何运作: 自组织临界性的科学
| publisher = Copernicus
| publisher = Copernicus
出版商哥白尼
| location = New York
| location = New York
| 地点: 纽约
| isbn = 978-0-387-94791-4
| isbn = 978-0-387-94791-4
[国际标准图书编号978-0-387-94791-4]
| author-link = Per Bak
| author-link = Per Bak
| 作者链接 Per Bak
}}
}}
}}
* {{cite journal
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]
| author = Bak, P. and Paczuski, M.
作者 Bak，p. and Paczuski，m。
| year = 1995
| year = 1995
1995年
| title = Complexity, contingency, and criticality
| title = Complexity, contingency, and criticality
| 标题复杂性、偶然性和临界性
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]
| journal = Proceedings of the National Academy of Sciences of the USA
美国美国国家科学院院刊杂志
| volume = 92
| volume = 92
第92卷
| pages = 6689–6696
| pages = 6689–6696
6689-- 6696
| url = http://pnas.org/cgi/content/abstract/92/15/6689
| url = http://pnas.org/cgi/content/abstract/92/15/6689
Http://pnas.org/cgi/content/abstract/92/15/6689
| doi = 10.1073/pnas.92.15.6689
| doi = 10.1073/pnas.92.15.6689
10.1073 / pnas. 92.15.6689
| pmid = 11607561
| pmid = 11607561
11607561
| issue = 15
| issue = 15
第15期
| pmc = 41396
| pmc = 41396
41396
|bibcode = 1995PNAS...92.6689B }}
|bibcode = 1995PNAS...92.6689B }}
92.6689 b }
* {{cite journal
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]
| author = Bak, P. and Sneppen, K.
作者 Bak，p. and Sneppen，k。
| year = 1993
| year = 1993
1993年
| title = Punctuated equilibrium and criticality in a simple model of evolution
| title = Punctuated equilibrium and criticality in a simple model of evolution
| 简单演化模型中的间断平衡和临界性
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 71
| volume = 71
第71卷
| issue = 24
| issue = 24
第24期
| pages = 4083–4086
| pages = 4083–4086
4083-- 4086
| doi = 10.1103/PhysRevLett.71.4083
| doi = 10.1103/PhysRevLett.71.4083
10.1103 / physrvlett. 71.4083
| pmid=10055149
| pmid=10055149
10055149
| bibcode=1993PhRvL..71.4083B}}
| bibcode=1993PhRvL..71.4083B}}
1993 phrvl. . 71.4083 b }
* {{cite journal
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| author = Bak, P., Tang, C. and Wiesenfeld, K.
作者 Bak，p. ，Tang，c. and Wiesenfeld，k。
| year = 1987
| year = 1987
1987年
| title = Self-organized criticality: an explanation of <math>1/f</math> noise
| title = Self-organized criticality: an explanation of <math>1/f</math> noise
| 题目自组织临界性: 数学噪音的解释
| journal = [[Physical Review Letters]]
| journal = Physical Review Letters
物理评论快报
| volume = 59
| volume = 59
第59卷
| issue = 4
| issue = 4
第四期
| pages = 381–384
| pages = 381–384
381-- 384
| doi = 10.1103/PhysRevLett.59.381
| doi = 10.1103/PhysRevLett.59.381
10.1103 / physrvlett. 59.381
| pmid = 10035754
| pmid = 10035754
10035754
| bibcode=1987PhRvL..59..381B}}
| bibcode=1987PhRvL..59..381B}}
1987 / phrvl. . 59. . 381 b }
* {{cite journal
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| author = Bak, P., Tang, C. and Wiesenfeld, K.
作者 Bak，p. ，Tang，c. and Wiesenfeld，k。
| year = 1988
| year = 1988
1988年
| title = Self-organized criticality
| title = Self-organized criticality
标题自组织临界性
| journal = [[Physical Review A]]
| journal = Physical Review A
物理评论 a 期刊
| volume = 38
| volume = 38
第38卷
| issue = 1
| issue = 1
第一期
| pages = 364–374
| pages = 364–374
364-- 374
| doi = 10.1103/PhysRevA.38.364
| doi = 10.1103/PhysRevA.38.364
10.1103 / PhysRevA. 38.364
| pmid = 9900174
| pmid = 9900174
9900174
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。
* {{cite book
| author = Buchanan, M.
| author = Buchanan, M.
作者: 布坎南。
| year = 2000
| year = 2000
2000年
| title = Ubiquity
| title = Ubiquity
标题: Ubiquity
| publisher = Weidenfeld & Nicolson
| publisher = Weidenfeld & Nicolson
| publisher = Weidenfeld & Nicolson
| location = London
| location = London
地点: 伦敦
| isbn = 978-0-7538-1297-6
| isbn = 978-0-7538-1297-6
[国际标准图书编号978-0-7538-1297-6]
| author-link = Mark Buchanan
| author-link = Mark Buchanan
马克 · 布坎南
}}
}}
}}
* {{cite book
| author = Jensen, H. J.
| author = Jensen, H. J.
作者 Jensen，h. j。
| year = 1998
| year = 1998
1998年
| title = Self-Organized Criticality
| title = Self-Organized Criticality
标题自组织临界性
| publisher = [[Cambridge University Press]]
| publisher = Cambridge University Press
出版商剑桥大学出版社
| location = Cambridge
| location = Cambridge
| 地点: 剑桥
| isbn = 978-0-521-48371-1
| isbn = 978-0-521-48371-1
[国际标准图书编号978-0-521-48371-1]
| author-link = Henrik Jeldtoft Jensen
| author-link = Henrik Jeldtoft Jensen
作者: 亨里克 · 耶尔德托夫特 · 詹森
}}
}}
}}
* {{cite journal
| author = Katz, J. I.
| author = Katz, J. I.
作者 Katz，j. i。
| year = 1986
| year = 1986
1986年
| title = A model of propagating brittle failure in heterogeneous media
| title = A model of propagating brittle failure in heterogeneous media
在非均匀介质中传播脆性破坏的模型
| journal = Journal of Geophysical Research
| journal = Journal of Geophysical Research
地球物理研究期刊
| bibcode = 1986JGR....9110412K
| bibcode = 1986JGR....9110412K
| bibcode 1986JGR... 9110412K
| doi = 10.1029/JB091iB10p10412
| doi = 10.1029/JB091iB10p10412
| doi 10.1029 / JB091iB10p10412
| volume = 91
| volume = 91
第91卷
| issue = B10
| issue = B10
第10期
| pages = 10412
| pages = 10412
10412页
}}
}}
}}
* {{cite journal
| author = Kron, T./Grund, T.
| author = Kron, T./Grund, T.
作者: Kron t. / Grund t。
| year = 2009
| year = 2009
2009年
| title = Society as a Selforganized Critical System
| title = Society as a Selforganized Critical System
作为一个自组织的批判系统的社会
| journal = Cybernetics and Human Knowing
| journal = Cybernetics and Human Knowing
控制论与人类认知
| volume = 16
| volume = 16
第16卷
| pages = 65–82
| pages = 65–82
第65-82页
}}
}}
}}
* {{Cite book
| author = Paczuski, M.
| author = Paczuski, M.
作者: 帕祖斯基。
| year = 2005
| year = 2005
2005年
| title = Networks as renormalized models for emergent behavior in physical systems
| title = Networks as renormalized models for emergent behavior in physical systems
作为物理系统中突发行为的重整化模型的网络
| journal = Complexity
| journal = Complexity
杂志复杂性
| pages = 363–374
| pages = 363–374
第363-374页
| arxiv = physics/0502028
| arxiv = physics/0502028
| arxiv physics / 0502028
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042
| series = The Science and Culture Series – Physics
| series = The Science and Culture Series – Physics
| 科学与文化系列-物理学
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886
| author-link = Maya Paczuski
| author-link = Maya Paczuski
| 作者链接 Maya Paczuski
}}
}}
}}
* {{cite book
| author = Turcotte, D. L.
| author = Turcotte, D. L.
作者: Turcotte，D.l。
| year = 1997
| year = 1997
1997年
| title = Fractals and Chaos in Geology and Geophysics
| title = Fractals and Chaos in Geology and Geophysics
地质学与地球物理学中的分形与混沌
| publisher = [[Cambridge University Press]]
| publisher = Cambridge University Press
出版商剑桥大学出版社
| location = Cambridge
| location = Cambridge
| 地点: 剑桥
| isbn = 978-0-521-56733-6
| isbn = 978-0-521-56733-6
[国际标准图书馆编号978-0-521-56733-6]
| author-link = Donald L. Turcotte
| author-link = Donald L. Turcotte
作者: Donald l. Turcotte
}}
}}
}}
* {{cite journal
| author = Turcotte, D. L.
| author = Turcotte, D. L.
作者: Turcotte，D.l。
| year = 1999
| year = 1999
1999年
| title = Self-organized criticality
| title = Self-organized criticality
标题自组织临界性
| journal = [[Reports on Progress in Physics]]
| journal = Reports on Progress in Physics
物理学进展报告
| volume = 62
| volume = 62
第62卷
| issue = 10
| issue = 10
第10期
| pages = 1377–1429
| pages = 1377–1429
13771429页
| doi = 10.1088/0034-4885/62/10/201
| doi = 10.1088/0034-4885/62/10/201
10.1088 / 0034-4885 / 62 / 10 / 201
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte
}}
}}
}}
* {{cite journal
| author = Md. Nurujjaman/A. N. Sekar Iyengar
| author = Md. Nurujjaman/A. N. Sekar Iyengar
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar
| year = 2007
| year = 2007
2007年
| title = Realization of {SOC} behavior in a dc glow discharge plasma
| title = Realization of {SOC} behavior in a dc glow discharge plasma
直流辉光放电等离子体{ SOC }行为的实现
| journal = [[Physics Letters A]]
| journal = Physics Letters A
物理学快报
| volume = 360
| volume = 360
第360卷
| issue = 6
| issue = 6
第六期
| pages = 717–721
| pages = 717–721
717-- 721页
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar
| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar
}}
}}
}}
*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]
[[Category:Critical phenomena]]
Category:Critical phenomena
范畴: 关键现象
[[Category:Applied and interdisciplinary physics]]
Category:Applied and interdisciplinary physics
类别: 应用和跨学科物理学
[[Category:Chaos theory]]
Category:Chaos theory
范畴: 混沌理论
[[Category:Self-organization]]
Category:Self-organization
类别: 自我组织
<noinclude>
<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude>
[[Category:待整理页面]]