Synchronous Dynamics Analysis Of Complex Network Systems Under The Influence Of Noise

Complex networks,such as business networks,the Internet and neural networks,are universal in our daily lives.With the development of computer technology,the theory and application of complex network,especially the synchronization dynamics of complex networks,have attracted a growing number of researchers' attention.However,the majority of the existing research results fail to consider the noise and time delay in the complex network system.In this paper,we study the complete synchronization and cluster synchronization of high-dimensional complex network system using random dynamical system and stochastic simulation methods,revealing the key influence of noise and coupling delay on synchronization.The main contents and conclusions are as follows:1.The common noise induced complete synchronization in discrete chaotic network systems is studied.A network model that two uncoupled discrete chaotic networks with identical parameters under the excitation of external common noise is firstly constructed.Then,by virtue of the Birkhoff traversal theorem and matrix theory,some sufficient conditions for synchronization between the two discrete chaotic networks is rigorously derived.Then,with the aid of a specific chaotic network model,the effectiveness of the theoretical analysis is verified by applying multiple numerical simulations.By simulating the synchronization error and other indicators,we find that when the network model parameters satisfy the sufficient conditions of theoretical analysis,the common noise can induce two uncoupled chaotic networks with identical parameters to achieve full synchronization in a random sense,and that the synchronization is robust against topology variation of complex network.This research enriches the theoretical research results of noise induced synchronization,and helps to understand the positive effect of noise on the ordered dynamics of high-dimensional nonlinear chaotic systems.2.Effects of noise and coupling delay on the complete synchronization and cluster synchronization of neural networks under electromagnetic induction are investigated.We construct a neural network model whose network topology is of NW small-world property and whose local node is Hindmarsh-Rose(HR)neuron under electromagnetic induction.Firstly,we investigate the complete synchronization characteristics of the HR neural network under noises.The stochastic simulation results show that electromagnetically uncoupled and weakly coupled HR neurons can be induced by noises to achieve complete synchronization.Secondly,we study the cluster synchronization characteristics of neural networks and find that larger coupled strength can induce HR neuron networks to achieve cluster synchronization.Furthermore,we find that cluster synchronization occurs intermittently with increasing coupled delay,i.e.coupled delay is capable of inducing cluster synchronous transition.Finally,we investigate the impact of noises on cluster synchronous transition,and come to the conclusion that strong noises inhibit the cluster synchronous transition.