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[[File:Hou710 BooleanNetwork.svg|thumb|State space of a Boolean Network with ''N=4'' [[Vertex (graph theory)|nodes]] and ''K=1'' [[Glossary of graph theory#Basics|links]] per node. Nodes can be either switched on (red) or off (blue). Thin (black) arrows symbolise the inputs of the [[Boolean function]] which is a simple "copy"-function for each node. The thick (grey) arrows show what a synchronous update does. Altogether there are 6 (orange) [[attractor]]s, 4 of them are [[Fixed point (mathematics)|fixed points]].|链接=Special:FilePath/Hou710_BooleanNetwork.svg]]
[[File:Hou710 BooleanNetwork.svg|thumb|State space of a Boolean Network with ''N=4'' [[Vertex (graph theory)|nodes]] and ''K=1'' [[Glossary of graph theory#Basics|links]] per node. Nodes can be either switched on (red) or off (blue). Thin (black) arrows symbolise the inputs of the [[Boolean function]] which is a simple "copy"-function for each node. The thick (grey) arrows show what a synchronous update does. Altogether there are 6 (orange) [[attractor]]s, 4 of them are [[Fixed point (mathematics)|fixed points]].|链接=Special:FilePath/Hou710_BooleanNetwork.svg]]
<font color="#FF8000">布尔函数Boolean function</font>是一种可用于通过逻辑类型的计算来评估与其布尔输入有关的任何布尔输出的函数。这些功能在复杂性理论中起着基本作用。
'''<font color="#FF8000">布尔函数Boolean function</font>'''是一种可用于通过逻辑类型的计算来评估与其布尔输入有关的任何布尔输出的函数。这些功能在复杂性理论中起着基本作用。当布尔函数应用于复杂网络中时，我们定义了'''<font color="#FF8000">布尔网络 Boolean Network </font>'''的概念：布尔网络是由一组离散的布尔变量组成，每个变量都被分配了一个布尔函数（可能每个变量都不同），它从这些变量的子集中获取输入，并输出决定其被分配的变量的状态。 这一组函数实际上决定了变量集上的拓扑结构（连通性），这些变量就成为网络中的节点。每个变量的状态都由二进制1（开）和0（关）表示，每个模型都有着对应的逻辑规则表，每个变量的邻接变量可以在逻辑规则表的作用下得到自己的状态。由布尔表达式即可看出各个变量之间的逻辑关系。通常，系统的动态是以离散时间序列的形式进行的，通过评估每个变量在时间 ''t'' 的网络状态上的函数来确定整个网络在时间 ''t+1''的状态，这可能是同步或异步完成的<ref>{{cite journal|last1=Naldi|first1=A.|last2=Monteiro|first2=P. T.|last3=Mussel|first3=C.|last4=Kestler|first4=H. A.|last5=Thieffry|first5=D.|last6=Xenarios|first6=I.|last7=Saez-Rodriguez|first7=J.|last8=Helikar|first8=T.|last9=Chaouiya|first9=C.|title=Cooperative development of logical modelling standards and tools with CoLoMoTo|journal=Bioinformatics|date=25 January 2015|volume=31|issue=7|pages=1154–1159|doi=10.1093/bioinformatics/btv013|pmid=25619997|doi-access=free}}<nowiki></ref>。
'''<font color="#FF8000">布尔网络 Boolean Network </font>'''由一组离散的布尔变量组成，每个变量都被分配了一个布尔函数（可能每个变量都不同），它从这些变量的子集中获取输入，并输出决定其被分配的变量的状态。 这一组函数实际上决定了变量集上的拓扑结构（连通性），这些变量就成为网络中的节点。通常，系统的动态是以离散时间序列的形式进行的，通过评估每个变量在时间 ''t'' 的网络状态上的函数来确定整个网络在时间 ''t+1''的状态，这可能是同步或异步完成的<ref>{{cite journal|last1=Naldi|first1=A.|last2=Monteiro|first2=P. T.|last3=Mussel|first3=C.|last4=Kestler|first4=H. A.|last5=Thieffry|first5=D.|last6=Xenarios|first6=I.|last7=Saez-Rodriguez|first7=J.|last8=Helikar|first8=T.|last9=Chaouiya|first9=C.|title=Cooperative development of logical modelling standards and tools with CoLoMoTo|journal=Bioinformatics|date=25 January 2015|volume=31|issue=7|pages=1154–1159|doi=10.1093/bioinformatics/btv013|pmid=25619997|doi-access=free}}<nowiki></ref>。
布尔网络在生物学中已被用于模拟'''<font color="#FF8000">调节网络 Regulatory Networks </font>'''。虽然布尔网络是对遗传现实的粗略简化，基因不是简单的二进制开关，但在一些情况下，它们正确地捕捉了表达和抑制基因的正确模式<ref>{{cite journal|last1=Albert|first1=Réka|last2=Othmer|first2=Hans G|title=The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster|journal=Journal of Theoretical Biology|date=July 2003|volume=223|issue=1|pages=1–18|doi=10.1016/S0022-5193(03)00035-3|pmid=12782112|pmc=6388622|citeseerx=10.1.1.13.3370}}<!--|accessdate=25 November 2014--></ref><ref>{{cite journal|last1=Li|first1=J.|last2=Bench|first2=A. J.|last3=Vassiliou|first3=G. S.|last4=Fourouclas|first4=N.|last5=Ferguson-Smith|first5=A. C.|last6=Green|first6=A. R.|title=Imprinting of the human L3MBTL gene, a polycomb family member located in a region of chromosome 20 deleted in human myeloid malignancies |journal=Proceedings of the National Academy of Sciences|date=30 April 2004 |volume=101|issue=19 |pages=7341–7346 |doi=10.1073/pnas.0308195101|pmid=15123827 |pmc=409920|bibcode = 2004PNAS..101.7341L }}</ref>。
布尔网络在生物学中已被用于模拟'''<font color="#FF8000">调节网络 Regulatory Networks </font>'''。虽然布尔网络是对遗传现实的粗略简化，基因不是简单的二进制开关，但在一些情况下，它们正确地捕捉了表达和抑制基因的正确模式<ref>{{cite journal|last1=Albert|first1=Réka|last2=Othmer|first2=Hans G|title=The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster|journal=Journal of Theoretical Biology|date=July 2003|volume=223|issue=1|pages=1–18|doi=10.1016/S0022-5193(03)00035-3|pmid=12782112|pmc=6388622|citeseerx=10.1.1.13.3370}}<!--|accessdate=25 November 2014--></ref><ref>{{cite journal|last1=Li|first1=J.|last2=Bench|first2=A. J.|last3=Vassiliou|first3=G. S.|last4=Fourouclas|first4=N.|last5=Ferguson-Smith|first5=A. C.|last6=Green|first6=A. R.|title=Imprinting of the human L3MBTL gene, a polycomb family member located in a region of chromosome 20 deleted in human myeloid malignancies |journal=Proceedings of the National Academy of Sciences|date=30 April 2004 |volume=101|issue=19 |pages=7341–7346 |doi=10.1073/pnas.0308195101|pmid=15123827 |pmc=409920|bibcode = 2004PNAS..101.7341L }}</ref>。
==Classical model==
== Classical model==
经典模型<br>
经典模型<br>
!年份
!年份
!Mean attractor length
! Mean attractor length
!Mean attractor length
!Mean attractor length
!comment
!comment
! 评论
!评论
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|Bastolla/ Parisi<ref name="BastollaParisi1998">{{cite journal|last1=Bastolla|first1=U.|last2=Parisi|first2=G.|title=The modular structure of Kauffman networks|journal=Physica D: Nonlinear Phenomena|date=May 1998|volume=115|issue=3–4|pages=219–233|doi=10.1016/S0167-2789(97)00242-X|arxiv = cond-mat/9708214 |bibcode = 1998PhyD..115..219B }}<!--|accessdate=26 November 2014--></ref>
| Bastolla/ Parisi<ref name="BastollaParisi1998">{{cite journal|last1=Bastolla|first1=U.|last2=Parisi|first2=G.|title=The modular structure of Kauffman networks|journal=Physica D: Nonlinear Phenomena|date=May 1998|volume=115|issue=3–4|pages=219–233|doi=10.1016/S0167-2789(97)00242-X|arxiv = cond-mat/9708214 |bibcode = 1998PhyD..115..219B }}<!--|accessdate=26 November 2014--></ref>
|Bastolla/ Parisi
|Bastolla/ Parisi
|Bilke/ Sjunnesson<ref>{{cite journal|last1=Bilke|first1=Sven|last2=Sjunnesson|first2=Fredrik|title=Stability of the Kauffman model|journal=Physical Review E|date=December 2001|volume=65|issue=1|pages=016129|doi=10.1103/PhysRevE.65.016129|pmid=11800758|arxiv = cond-mat/0107035 |bibcode = 2002PhRvE..65a6129B }}<!--|accessdate=26 November 2014--></ref>
|Bilke/ Sjunnesson<ref>{{cite journal|last1=Bilke|first1=Sven|last2=Sjunnesson|first2=Fredrik|title=Stability of the Kauffman model|journal=Physical Review E|date=December 2001|volume=65|issue=1|pages=016129|doi=10.1103/PhysRevE.65.016129|pmid=11800758|arxiv = cond-mat/0107035 |bibcode = 2002PhRvE..65a6129B }}<!--|accessdate=26 November 2014--></ref>
|Bilke/ Sjunnesson
| Bilke/ Sjunnesson
|Bilke/Sjunnesson
|Bilke/Sjunnesson
|superpolynomial growth, <math>\langle\nu\rangle > N^x \forall x</math>
|superpolynomial growth, <math>\langle\nu\rangle > N^x \forall x</math>
| 超多项式生长，< math > langle nu rangle > n ^ x for all x <nowiki></math ></nowiki>
|超多项式生长，< math > langle nu rangle > n ^ x for all x <nowiki></math ></nowiki>
|mathematical proof
|mathematical proof
|faster than a power law, <math>\langle A\rangle > N^x \forall x</math>
|faster than a power law, <math>\langle A\rangle > N^x \forall x</math>
| faster than a power law, <math>\langle A\rangle > N^x \forall x</math>
|faster than a power law, <math>\langle A\rangle > N^x \forall x</math>
|比幂定律快，< math > langle a rangle > n ^ x for all x <nowiki></math ></nowiki>
|比幂定律快，< math > langle a rangle > n ^ x for all x <nowiki></math ></nowiki>
|faster than a power law, <math>\langle\nu\rangle > N^x \forall x</math>
|faster than a power law, <math>\langle\nu\rangle > N^x \forall x</math>
|faster than a power law, <math>\langle\nu\rangle > N^x \forall x</math>
| faster than a power law, <math>\langle\nu\rangle > N^x \forall x</math>
|比幂定律快，< math > langle nu rangle > n ^ x for all x <nowiki></math ></nowiki>
|比幂定律快，< math > langle nu rangle > n ^ x for all x <nowiki></math ></nowiki>