Dynamic Recovery Of Cascade Failures In Edge-coupled Interdependent Networks

In the real world,various infrastructure networks(such as energy,transportation,communication,etc.)and even social networks are interdependent and collaborative.Such networks with interdependencies can be called interdependent networks.The interdependencies between networks improve the overall operating efficiency of the networks and also enhance the vulnerability of the networks.Once the collapse of these infrastructure networks or social relations networks occurs,it will inevitably have an extremely important impact on social economic activities and people’s livelihoods.Therefore,how to improve the robustness of interdependent networks,effectively deal with and control failure propagation,avoid the occurrence of structural fracture of dependent networks,and how quickly and effectively recover the networks after the occurrence of structural fracture of interdependent networks has become a research hotspot in the field of complex network research.Traditional researches are mainly based on node-coupled interdependent networks,but there are also edge-coupled interdependent networks in the real world.At present,there is a lack of research on this kind of interdependent networks.Therefore,this paper carries out research on cascading failures recovery based on edge-coupled dependent networks.The main research work of this paper is as follows:(1)Considering that the recovery and reconstruction of the real network are normally based on the huge components of the network that can still function.In this paper,the coupled edge is found through the giant component in the process of network cascade failure,and the boundary coupled edge is randomly recovered with probability γ.By using the nature of the boundary coupled edge that connects the failed node and the interdependent networks giant component,the failed node and the failed edge of the recovery will not be easily to fail again in the subsequent cascade failure process.Through generation function and self-balancing probability theory,the cascade failure and recovery process of the edge-coupled interdependent networks are analyzed.It is found that the recovery model based on the boundary coupled edge can recover the interdependent networks,with 1-p proportional edge failure,to the initial state,but there is a critical probability of recovery,below which the network will collapse.(2)This paper studies recovery strategies that can take effect earlier with a larger initial edge failure ratio,or can restore the network to its initial state with fewer iteration steps.It is found that in ER-ER or SF-SF edge-coupled dependent networks under random faults,the selective recovery strategy based on edge betweenness(SREB)can take effect under a larger initial edge failure ratio.However,when the initial edge failure ratio is less than a certain value,each recovery strategy can recover the networks to the initial state.In this case,in ER-ER networks,the improved selective recovery strategy based on compound excessive degree(ISRCED)proposed in this paper can recover the networks to the initial state faster with fewer iteration steps,while the recovery strategy requiring fewer iteration steps in SF-SF networks is SREB.In the case of deliberate attack,in the ER-ER network,ISRCED takes effect earlier and can restore the network to the initial state faster.In the SF-SF network,SREB takes effect earlier and has the least iteration steps in the earlier effective stage.However,when the initial edge failure ratio is less than a certain value,the improved composite redundancy optimal recovery strategy can restore the network to the initial state more quickly.