Liu Run-Ran, Wang Wen-Xu, Lai Ying-Cheng, Wang Bing-Hong
Institute for Information Economy, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 2):026110. doi: 10.1103/PhysRevE.85.026110. Epub 2012 Feb 16.
In a complex network, random initial attacks or failures can trigger subsequent failures in a cascading manner, which is effectively a phase transition. Recent works have demonstrated that in networks with interdependent links so that the failure of one node causes the immediate failures of all nodes connected to it by such links, both first- and second-order phase transitions can arise. Moreover, there is a crossover between the two types of transitions at a critical system-parameter value. We demonstrate that these phenomena can occur in the more general setting where no interdependent links are present. A heuristic theory is derived to estimate the crossover and phase-transition points, and a remarkable agreement with numerics is obtained.
在复杂网络中，随机的初始攻击或故障能够以级联方式触发后续故障，这实际上是一种相变。近期研究表明，在具有相互依存链路的网络中，一个节点的故障会立即导致通过此类链路与之相连的所有节点的故障，一阶和二阶相变都可能出现。此外，在一个临界系统参数值处，这两种类型的相变之间存在交叉。我们证明，在不存在相互依存链路的更一般情况下，这些现象也会发生。我们推导了一种启发式理论来估计交叉点和相变点，并与数值计算结果取得了显著一致。
