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有关复杂网络攻击耐受性的更多详细信息,请参阅攻击耐受性页面。
 
有关复杂网络攻击耐受性的更多详细信息,请参阅攻击耐受性页面。
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==Cascading failures==
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== Cascading failures 连锁故障 ==
    
{{Main article|Cascading failure}}
 
{{Main article|Cascading failure}}
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An important aspect of failures in many networks is that a single failure in one node might induce failures in neighboring nodes. When a small number of failures induces more failures, resulting in a large number of failures relative to the network size, a [[cascading failure]] has occurred. There are many models for cascading failures. These models differ in many details, and model different physical propagation phenomenon from power failures to information flow over Twitter, but have some shared principals. Each model focuses on some sort of propagation or cascade, there is some threshold determining when a node will fail or activate and contribute towards propagation, and there is some mechanism defined by which propagation will be directed when nodes fail or activate. All of these models predict some critical state, in which the distribution of the size of potential cascades matches a power law, and the exponent is uniquely determined by the degree exponent of the underlying network. Because of the differences in the models and the consensus of this result, we{{Who|date=April 2015}} are led to believe the underlying phenomenon is universal and model-independent.
 
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An important aspect of failures in many networks is that a single failure in one node might induce failures in neighboring nodes. When a small number of failures induces more failures, resulting in a large number of failures relative to the network size, a [[cascading failure]] has occurred. There are many models for cascading failures.<ref>{{cite journal |last1=Dobson |first1=I. |last2=Carreras |first2=B. A. |last3=Lynch |first3=V. E. |last4=Newman |first4=D. E. |year=2007 |title=Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization |url=|journal=Chaos |volume=17 |issue=2|page=026103 |doi=10.1063/1.2737822|pmid=17614690 |bibcode=2007Chaos..17b6103D }}</ref><ref>{{cite journal |last1=Dobson |first1=I. |last2=Carreras |first2=A. |last3=Newman |first3=D.E. |year=|title=A loading dependent model of probabilistic cascading failure. Probability in the |url=|journal=Engineering and Informational Sciences |volume=19 |issue=15|page=2005 }}</ref><ref name="Watts2002">{{cite journal |last1=Watts |first1=D.J. |title=A simple model of global cascades on random networks |doi=10.1073/pnas.082090499 |pmid=16578874 |journal=PNAS |volume=99 |issue=9 |pages=5766–5771 |year=2002 |pmc=122850 |bibcode=2002PNAS...99.5766W }}</ref><ref>{{cite journal |last1=Goh |first1=K.-I. |last2=Lee |first2=D.-S. |last3=Kahng |first3=B. |last4=Kim |first4=D. |year=2003 |title=Sandpile on scale-free net-works |url=|journal=Phys. Rev. Lett. |volume=91 |issue=14|page=148701 |doi=10.1103/physrevlett.91.148701 |pmid=14611564 |bibcode=2003PhRvL..91n8701G|arxiv=cond-mat/0305425 }}</ref><ref>{{cite journal |last1=Lee |first1=D.-S. |last2=Goh |first2=K.-I. |last3=Kahng |first3=B. |last4=Kim |first4=D. |title=Sandpile avalanche dy-namics on scale-free networks |url=|journal=Physica A |volume=338 |issue=1–2 |page=84|year=2004 |doi=10.1016/j.physa.2004.02.028 |arxiv=cond-mat/0401531 |bibcode=2004PhyA..338...84L }}</ref><ref>{{cite journal |last1=Ding |first1=M. |last2=Yang |first2=W. |year=1995 |title=Distribution of the first return time in frac-tional Brownian motion and its application to the study of onoff intermit-tency |url=|journal=Phys. Rev. E |volume=52 |issue=1|pages=207–213 |doi=10.1103/physreve.52.207|pmid=9963421 |bibcode=1995PhRvE..52..207D }}</ref><ref>{{cite journal |last1=Motter |first1=Adilson E. |last2=Lai |first2=Ying-Cheng |title=Cascade-based attacks on complex networks |journal=Physical Review E |date=20 December 2002 |volume=66 |issue=6 |pages=065102 |doi=10.1103/PhysRevE.66.065102 |pmid=12513335 |arxiv=cond-mat/0301086|bibcode=2002PhRvE..66f5102M }}</ref><ref name="Kong2010">{{cite journal |last1=Kong |first1=Z. |last2=Yeh |first2=E. M. |title=Resilience to Degree-Dependent and Cascad-ing Node Failures in Random Geometric Networks |url=|journal=IEEE Transactions on Information Theory |volume=56 |issue=11 |page=5533|year=2010 |doi=10.1109/tit.2010.2068910}}</ref> These models differ in many details, and model different physical propagation phenomenon from power failures to information flow over Twitter, but have some shared principals. Each model focuses on some sort of propagation or cascade, there is some threshold determining when a node will fail or activate and contribute towards propagation, and there is some mechanism defined by which propagation will be directed when nodes fail or activate. All of these models predict some critical state, in which the distribution of the size of potential cascades matches a power law, and the exponent is uniquely determined by the degree exponent of the underlying network. Because of the differences in the models and the consensus of this result, we{{Who|date=April 2015}} are led to believe the underlying phenomenon is universal and model-independent.<ref name="NetworkBook"/>
      
An important aspect of failures in many networks is that a single failure in one node might induce failures in neighboring nodes. When a small number of failures induces more failures, resulting in a large number of failures relative to the network size, a cascading failure has occurred. There are many models for cascading failures. These models differ in many details, and model different physical propagation phenomenon from power failures to information flow over Twitter, but have some shared principals. Each model focuses on some sort of propagation or cascade, there is some threshold determining when a node will fail or activate and contribute towards propagation, and there is some mechanism defined by which propagation will be directed when nodes fail or activate. All of these models predict some critical state, in which the distribution of the size of potential cascades matches a power law, and the exponent is uniquely determined by the degree exponent of the underlying network. Because of the differences in the models and the consensus of this result, we are led to believe the underlying phenomenon is universal and model-independent.
 
An important aspect of failures in many networks is that a single failure in one node might induce failures in neighboring nodes. When a small number of failures induces more failures, resulting in a large number of failures relative to the network size, a cascading failure has occurred. There are many models for cascading failures. These models differ in many details, and model different physical propagation phenomenon from power failures to information flow over Twitter, but have some shared principals. Each model focuses on some sort of propagation or cascade, there is some threshold determining when a node will fail or activate and contribute towards propagation, and there is some mechanism defined by which propagation will be directed when nodes fail or activate. All of these models predict some critical state, in which the distribution of the size of potential cascades matches a power law, and the exponent is uniquely determined by the degree exponent of the underlying network. Because of the differences in the models and the consensus of this result, we are led to believe the underlying phenomenon is universal and model-independent.
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在许多网络中,失败的一个重要方面是一个节点的单一失败可能会导致相邻节点的失败。当少量的故障导致更多的故障,导致相对于网络大小的大量故障时,就会发生级联故障。对于连锁故障有许多模型。这些模型在许多细节上有所不同,并且模拟了从电源故障到 Twitter 上的信息流等不同的物理传播现象,但是有一些共享的原则。每个模型都关注于某种传播或级联,有一些阈值来决定一个节点何时会失败或激活并促进传播,还有一些机制定义了当节点失败或激活时,传播将被定向。所有这些模型都预测了一些临界状态,在这些临界状态中,势级联的大小分布符合幂律,指数由底层网络的度指数唯一决定。由于模型之间的差异和对这一结果的共识,我们相信潜在的现象是普遍的和模型独立的。
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在众多网络产生故障的时候会出现一个重要现象,即某单个节点的单个故障可能会引起相邻节点的故障。继而发生少量故障导致更多故障的连锁反应,当最终规模达到近似相对于该网络规模的大量故障时,就发生了连锁故障现象。连锁故障有很多模型。这些模型在很多细节上并不相同,从电网故障到Twitter上的信息流的传播,研究者们对不同物理传播现象均尝试过进行建模,发现其中具有部分可共享的原理。每个模型都专注于某种传播方式或级联反应,有一些阈值确定节点何时将发生故障或被激活,进而有助于传播。并且通过定义某种机制,使得节点发生故障或激活时将产生定向传播。所有这些模型都预测了某种临界状态,其中潜在级联的大小分布与幂律是相匹配的,并且其指数是由基础网络的度指数唯一确定。有关建模连锁故障的更多详细信息,请参阅全局连锁模型页面。
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For more detailed information on modeling cascading failures, see the global cascades model page.
 
For more detailed information on modeling cascading failures, see the global cascades model page.
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有关对级联故障建模的详细信息,请参阅全局级联模型页面。
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有关建模连锁故障的更多详细信息,请参阅全局连锁模型页面。
 
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==References==
 
==References==
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