Research On The Robustness Under Targeted Attacks And Recovery Of Directed Networks

Complex networks are widely used in various fields,such as sociology,economics,and biology,to study the functions and properties of systems.Robustness is one of the important properties of complex networks.Network robustness is influenced by many factors,such as network directionality,number of layers of the network,dependencies,attack methods,and self-recovery of nodes.Most previous studies are limited to the robustness of single-layer networks,multilayer undirected networks,or multilayer directed networks under random attacks,however,many real networks are directed.This thesis focuses on the research of the robustness of two-layer and multi-layer directed networks under targeted attacks and the robustness of directed networks with recovery.Also,the corresponding theoretical frameworks for analyzing the robustness of these systems are developed.Simulation results on Erd?s-Rény(ER)networks and Scale-free(SF)networks confirm the theoretical framework.The main research contents and results are as follows.A method is proposed to analyze the robustness of two-layer interdependent directed networks under two types of targeted attacks,namely,degree–based attacks and indegree/out-degree–based attacks.The method can predict the proportion of functional nodes at steady state,the percolation threshold,and the critical coupling strength of the system.It is found that degree–based attacks can perform more efficiently in breakdown the system than in-degree/out-degree–based attacks.For the interdependent ER network,four kinds of phase transitions,a four-phase point,and a two-phase point,are found in the phase diagram.For interdependent directed SF networks,no collapse phase transition is found in phase diagrams,and system robustness first increases and then decreases as the degree heterogeneity increases.These findings help understand system robustness and enable the better design of robust infrastructure systems.A theoretical framework for analyzing the robustness of networks of directed networks under targeted attacks is proposed.The framework is applied to treelike networks of directed networks and random regular networks of directed networks.It is found that the robustness of the system decreases sharply as the number of the networks in the system increases.For the random regular network of directed ER networks,the first-order phase transition and the hybrid phase transition disappear when the number of network is large.For the random regular network of directed SF networks,the collapse phase transition occurs only when the number of the network is larger than 3.A network robustness analysis method based on mean-field theory is proposed for the directed networks with spontaneous recovery.The method can predict the fraction of active nodes and the critical point of phase transition in the network.When the nodes of the directed network can recover from failure,the system shows a strong hysteresis phenomenon.For small-scale networks,the system exhibits a flipping phenomenon,that is,the fraction of active nodes switches back and forth between high and low states.Analyzing the differences between the directed and undirected networks,it is found that the introduction of directionality reduces the robustness of the system.