Robustness Analysis Of The Couple Network Based On The Relevance Of Nodes And Flows

With the increasing complexity and heterogeneity of network strctures,and diversification of network services in the real world,the coupled networks represented by the cyber physical system has gradually replaced the "individual" networks with single structure and function.However,the deep coupling between the two layers of coupled networks and the mutual differentiation also bring a series of problems.For example,a single failure in the coupled networks will transform the failure based on the strong coupling relationship,thereby causing more serious level of cascading failures;some flows in the network are related to nodes,and this relevance will increase the cross-regional propagation of failures.The traditional robustness analysis of complex networks is mostly based on the relevance between pairs or clusters of nodes.On the one hand,it is difficult to describe the effects of flows on the robustness.On the other hand,at the level of robustness optimization,the flows-based control mechanisms are not considered,which has certain limitations.Aiming at the shortcomings of existing research,this paper explores the robustness of the coupled networks,and provides robustness optimization and protection measures for coupled networks based on complex network theory and the relevance of nodes and flows.The main research contents are as follows:Firstly,a model of the coupled networks based on the relevance of nodes and flows is built,and its failure propagation process is described based on the theory of generating function.By simulating and analyzing the proportion of the giant component of the remaining network after the failure propagation,this paper finds that:on the one hand,the relevance of the nodes and the flows leads to the topology differences between the two layers,on the other hand,it also leads to the differences in the degree of influence of the failure propagation intensity on the stability and security of the whole system in the coupled networks during the failure propagation process.By comparing with the results of traditional coupled network researches,this paper finds that failure propagation based on the relevance of nodes and flows aggravates the intensity of failure at various stages of failure propagation,which greatly affects the robustness of the whole system.Then,based on the robustness analysis results of the coupled networks based on the relevance of nodes and flows,this paper explores the network protection measures and robustness optimization schemes.For the attacked flows in cascading failure,this paper adopts five different flow control strategies to reduce the strength of cascading failure based on the relevance of nodes and flows,aiming to improve the robustness of the network and propose reasonable robustness optimization recommendations based on the simulation results.This paper finds that even if it can be highly compatible with some flow control strategies,the nodes with large degree of BA scale-free network will still aggravate the strength of cascading failure and have a negative effect on network robustness;by adopting Dijkstra strategy and NSR strategy can significantly improve the robustness of the BA+BA coupling network based on node and flow association,and the ER+ER coupling network based on node and flow association,respectively.