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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。

==Cascading failures==

== Cascading failures 连锁故障 ==

{{Main article|Cascading failure}}

{{Main article|Cascading failure}}

 

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.

 

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.

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.

 

 

==References==

==References==