The Influence Of Weak Interdependent Groups On Cascade Failure Dynamics Of Complex Networks

In many real complex systems,while the nodes maintaining the overall function of the network through connection relationships,they may also form "interdependent groups" through some implicit relationships.It is of great practical significance and scientific value to investigate the influence of those "interdependent groups" on the cascading failure dynamics and robustness of networks.In those real networks,the interdependent intensity within the "interdependent groups" is "weak".In other words,the failure of a node is only destroy a part of the function of the another nodes in the same group,rather than destroy the coupling nodes thoroughly.In this thesis,we present a concept of "weak interdependent groups",and investigate the effects of the different features of the interdependent groups on the cascading dynamics and the robustness of complex networks.This main research and innovation of thesis is as follows:(1)A network cascading failure model with "weak interdependent groups" is proposed.By considering the diversity of interdependent intensity in different networks,the thesis introduces a decoupling coefficient ? to control the interdependent intensity between nodes within the group in the network model.It can be found that the cascading failure of the network model depends on the decoupling coefficient ?.When the value of ? is large,the network can show strong robustness and invulnerability,and the avalanche process after being attacked is relatively mild,showing the second-order phase transition.When the value of ? is small,the robustness of the network is relatively weak,and the avalanche process is relatively rapid and sudden,showing the first-order phase transition.(2)The effects of the interdependent intensity,size and distribution of "weak interdependent groups" in random network and scale-free network on the cascading dynamics and robustness of network are studied.Through the analysis of simulation experiment and theoretical results,it is found that the smaller the interdependent group size is,and the weaker the interdependent intensity between nodes within the group is,the better the network robustness is.In addition,the analytical results show that the network with non-uniform distributed interdependent groups is more robust than the network with uniform distributed interdependent groups.(3)Empirical network verification.This thesis conducts numerical experiments by using our model in the "Email-Eu-core" and "American College football" two real networks to verify the consistence of the model.The results show that in these two real networks,the degree of interdependence between nodes within the "weak interdependent group" will affect the robustness of the network.The stronger the interdependent intensity between nodes,the network becomes more vulnerable.On the contrary,the weaker the interdependent intensity,the network becomes more robust.In this thesis,we reveal the characteristics of cascading failure process and robustness of the network with "weak interdependent groups" through theoretical analysis and numerical simulation.At the scale level,the cascading failure of the network with "weak interdependent groups" can be divided into two processes: "intra-group cascading" and "inter-group cascading".Under the synergistic effects of these two processes,the network will cascade failure after deleted some nodes.At the same time,the conclusions obtained in this thesis shows that controlling the characteristics of "weak interdependent groups" can avoid the system to be collapsed suddenly and improve the robustness of the network,which provides some inspirations for how to design a network with an ideal resilience.