Research On Robustness Of Multilayer Networks

Complex systems such as social systems,information systems,and military systems exhibit significant hierarchical,differential,and dynamic characteristics.The traditional single layer network model cannot fully describe the above complexity,and it is especially necessary to study multilayer networks characterizing interlayer coupling,structural differences and dynamical evolution.Network robustness is one of the core issues of network science.Studies on the robustness of multilayer networks is more challenging,and it has become a frontier topic in the development of network science.This thesis focuses on roubstness of multilayer networks exploiting the percolation theory and studies the coupling mechanism of multilayer networks,attack cascade failure and structural state recovery.Specifically includes the following four aspects:Firstly,for the problem of multilayer network coupling mechanism,the multilayer network core percolation model is proposed.The model extends core percolation to the multilayer network,and theoretically derives the evolution equation of degree distribution in the multilayer network core percolation process,revealing the first-order phase transition phenomenon of multilayer networks against core percolation,that is,the core structure emerges at the critical point in a discontinuous way.According to the analysis of the evolution equation,this discontinuous emergence is origined from the multilayer network interlayer coupling interactions and the diversity of leaf nodes.The experimental results on a variety of typical network structure models are agree with the theoretical predictions of the model,which verifies the correctness of theory.This model illustrates the structural evolution of a multilayer network under core percolation.Secondly,for the cooperative attack modeling on multilayer networks,the combined attack model is proposed.The model adopts a combined attack strategy for different layers,and develops a mathematical analysis framework for multilayer network against cooperative attack and cascade failure.The critical point for breakdown multilayer networks and the fraction of the giant component are derived by theory equations.It can be calculated from the equation that the combination of targeted attack and localized attack is the most effective attack mode,that is,the minimum fraction of nodes to be removed to breakdown the networks.The experimental results are agree with the prediction results of the model theory,which verifies the correctness of theory.This model illustrates collaborative attack effect and attack selection strategy on multilayer networks.Thirdly,for the attack modeling problem of multilayer networks under constraints,the limited information intentional attack model is proposed.The model assumes that only the limited node structure information is known.The critical point of the singlelayer and multilayer network under the intentional attack and the fraction of corresponding network giant component are obtained by theory equations,which describes the quantitative relationships between the known node information and network damage.We found the existence of the critical information thresholds,that is,As the threshold is exceeded,the impact of the limited information attack on the network structure does not change much.The experimental results on both the simulation and empirical networks verify the existence of theoretically predicted critical information threshold.Further,considering both the information and spatial constraints,similar conclusions are obtained.This model illustrates the network attack information utilization strategy under limited information conditions.Fourthly,for node state recovery modeling problem on multilayer networks,the dynamic network failure recovery model is proposed.The model considers that node failure and recovery are affected by the node itself and neighbor nodes.The evolution equation describing network state is established,and a stochastic simulation method suitable for large-scale network node failure and recovery process is designed.The simulation experiments are carried on the random regular network and spatial embedded network.Considering the influence of two failure rate factors of the node itself and neighbor nodes,it is found that there exists a metastable region and two steady-state regions in the network.Adjusting the initial state of networks and the change path of failure rate,the transition from the metastable state to the specified steady state is achieved.This model illustrates the failure recovery mechanism and control strategy on multilayer dynamic networks.