Recovery strategy of multilayer network against cascading failure

Cascading failure phenomena widely exist in real-life circumstances, such as the blackouts in power networks and the collapse in computer networks. In this paper, we construct a cascading failure model on the multilayer network, taking into account the number of invalid neighbors of nodes, the failure frequency of nodes, the effect between layers, and the percolation process. To minimize network losses caused by the cascading process, we propose a recovery strategy, i.e. repairing some certain clusters formed by ineffective nodes and links. The recovery strategy is discussed in detail, like whether to add links to the network, how many links are needed at least to add, how many layers are demanded to restore, and how to choose the values of g and restorable threshold ζ to improve the network performance. Besides, we theoretically analyze the cascading failure model with recovery strategy by virtue of mean-field approximation and generating function techniques. The theoretical solutions are found to be consistent with experimental results simulated on the ER as well as BA networks. In addition, we also investigate the affecting factors of network robustness. The effects of failure threshold α, base number f, and threshold φ between layers on network behaviors depend on the values of average degree 〈k〉 and recovery proportion θ. These results may provide particular reference significance for maintaining system security, adjusting the network performance, and enhancing network robustness.