Synchronization Of Several Kinds Of Complex Networks Via Aperiodically Intermittent Control

Complex networks are composed of a large number of nodes and the connections between nodes,which is ubiquitous in the real world,ranging from the Internet to mobile communication networks,power networks,biological networks,food chain networks,transportation networks,social networks and so on.The basic characteristics of complex networks include large and diverse nodes,complexity of structures and varying with time,interaction between structure and dynamics,and influence between different network systems.Coordination of complex networks is one of the important dynamic behaviors of networks,especially synchronization,which has become a hot topic in research fields in recent years.Researchers have proposed a variety of synchronization patterns,various control strategies to achieve synchronization of different networks,and amounts of excellent results have emerged.In this paper,on the basis of summarizing the current work on synchronization of complex networks,based on the aperiodically intermittent control strategy,synchronizations of three kinds of complex networks with time delay are discussed by using the knowledge of complex network theory,stability theory,matrix theory,stochastic differential equation theory,graph theory and so on.The specific research work is as follows:Firstly,the synchronization problem of a class of topological switched networks with time delays is studied,in which the topology is switched randomly in a finite number of modes,and the internal delays and coupling delays are closely related to the modes.By designing the Lyapunov function related to the topological mode,using aperiodically intermittent pinning control,applying the stability theory and differential inequality,and combining the properties of the average dwelling time of network modes,the sufficient conditions for the exponential synchronization of switched networks are obtained.Then,considering the limited channel information is restricted in real control,combining quantitative control and aperiodically intermittent control to discuss synchronization for a class of coupled system with system delays and coupling delays.Based on stability theory,Schur complement lemma,differential inequality and so on,the sufficient conditions for the synchronization are gained by designing the time-dependent Lyapunov function.The validity and efficiency of theoretical results are verified by numerical simulations.Finally,the mean square synchronization of a class of stochastic complex networks with time delay and uncertain terms under noise disturbance is discussed deeply.This network model not only contains time delay,but also is affected by network operation noise and uncertainty factors.It designs the non-periodic quantized intermittent pinning controller,selects Lyapunov function closely related to network topology structure,and organically combines stability theory,stochastic differential equation theory and graph theory,etc.,to obtain sufficient conditions for the network to achieve the mean square synchronization.