Research On Identification Of Edge Importance And Attack Robustness Of Interdependent Systems

More and more complex systems are emerging in nature and human society.As the scale of the system expands,it is at risk of being attacked or destroyed at any time.Therefore,it is particularly important to measure the importance of nodes and edges,identify key nodes and edges,and implement effective protection strategies.At the same time,complex systems in the real world often do not exist independently.There are various dependencies between multiple systems.The dependencies will cause attacks on a single system to spread to other systems,and then cause global collapse.Therefore,it has important theoretical significance and application value to study the cascading failure behavior caused when the interdependent network system is attacked,and to explore effective optimization and protection methods.Based on the above problems,the edge importance recognition method based on k-shell decomposition is proposed,which is effectively applied to network attacks and controllability.Two interdependent systems that suffer from different attacks are proposed,and the structural vulnerability of interdependent systems under the combined action of attack and optimization is studied.(1)Research on edge importance identification method based on k-shell decompositionTaking into account the problems of high computational complexity and weak discrimination in the existing measurement indicators,comprehensively considering the k-shell value and the difference between the nodes at both ends of the edge,an edge importance recognition method based on k-shell decomposition is proposed.Through numerical simulation,the effectiveness of the proposed method is verified for both network attacks and controllability applications in real and ER random networks.Research shows that the attack strategy that considers the difference and maximum value of the end node k-shell has an attack effect far exceeding other attack strategies;the edge betweenness attack has the most obvious effect in uniform networks such as power networks;With the increase of the average degree,the attack effect of the edge betweenness attack on the random network becomes worse.The application of the proposed method in network controllability is analyzed.When the difference and minimum value of the endpoint k-shell are used as the measure of edge importance,it can correspond to the edges necessary to control the network in most networks.The experimental results show that the proposed edge importance identification method can solve the problems of high computational complexity of edge importance and weak discrimination to a certain extent.(2)Analysis of structural vulnerability of interdependent systems under the combined action of attack and optimizationFirst of all,we propose a dependent system model under two different attack modes,direct and indirect,while considering network optimization problems,and extend the effective cross-reconnection method under a single network to interdependent systems.Through numerical simulation experiments,the cascade failure problem of two interdependent systems facing the targeted attack on nodes is analyzed.Research results shows that single network optimization plays a positive role in improving the attack robustness of the entire system.When the coupling strength of the dependent system is weak,the optimization effect can be improved,but as the coupling strength increases,the optimization effect decreases.The research conclusions can appropriately enrich the modeling methods and theoretical analysis of network attacks,and provide some scientific theoretical basis and feasibility suggestions for the prevention and control of cascading failure behaviors designing safe and reliable systems and optimizing of existing systems.