复杂网络中带有应急恢复机理的级联动力学分析*

摘要

提出带有应急恢复机理的网络级联故障模型，研究模型在最近邻耦合网络， Erdos-Renyi随机网络， Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为。给出了应急恢复机理和网络效率的定义，并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响。结果表明，模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度，并且提高了网络的恢复能力。而且网络中节点负载容量越大，网络效率降低速度和节点故障率的增长速度越慢。同时，随着节点过载故障概率的减小，网络效率的降低速度和节点故障率的增长速度也逐渐减缓。此外，对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析，结果发现网络拓扑节点度分布的异质化程度的增大，提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度。以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为，为实际网络中级联故障现象的控制和防范提供了参考。%A model of cascading failures in complex networks with an emergency recovery mechanism is proposed in this paper, and the cascading dynamics is investigated by running the proposed model on nearest-neighbor coupled network, Erdos-Renyi random graph network, Watts-Strogatz small-world network and Barabasi-Albert scale-free network respectively. New concepts in emergency recovery mechanism and the efficiency of networks are defined. And the effects of the parameters on the network efficiency and failure rate are investigated. Results demonstrate that the increase of the emergency recovery probability would reduce the network efficiency decreasing speed and the failure rate growing speed, and also improve the resilience of the network. And the greater the load capacity of the nodes in the network, the slower the speeds of network efficiency reducing and failure rate growing. Meanwhile, with the decrease of the overload node failure probability, the reducing speed of network efficiency and the growing speed of failure rate would reduce gradually. Furthermore, the changes of the network efficiency and failure rate during the process of cascading failures in different network topologies are analyzed. It is found that the rise of the heterogeneity of degree distribution increases the reducing speed of network efficiency and the growing speed of failure rate. All these results can help analyze the cascading dynamics in complex networks with an emergency recovery mechanism, and may provide a guidance for the controling of cascading failures and protecting against them in real-life complex networks.