Research On Synchronization Of Some Complex Networks And Its Control

A complex network is a set of coupled nodes interconnected by edges,in which each node represents a dynamical system.The structure of many real systems in nature can be described by the complex networks,such as social relationship networks,food chain,the World-Wide-Web,and so on.This has led to much interest to the studies of the complex networks.In particular,synchronization of the network has been one of the main topics due to its various applications.Based on the finite-time stability theory,by designing suitable controllers,constructing Lyapunov functional and employing evaluation of inequalities can derive several sufficient conditions about finite-time synchronization of complex networks,finally we will give numerical simulations to verify the effectiveness and feasibility results obtained here.This paper includes the following aspects:Firstly,according to finite-time stability theory and topology identification principle,for different models of complex networks with unknown parameters and time-varying delays,by proposing bidirectional coupling and non fragile feedback control,respectively,and combating their separate updated laws of parameters,not only complex networks can achieve finite-time(hybrid outer)synchronization,but also parameters can be identified in a finite time.Finally,numerical simulations verify the correctness of the results analyzed.Secondly,for the problem of complex networks with delays,by employing sliding mode control and periodically intermittent control,given sliding mode surface,by proposing periodically intermittent sliding mode feedback controllers and periodically intermittent sliding mode bidirectional control strengths,respectively,combating the finite-time stability theory,not only complex networks can achieve finite-time lag synchronization,but also the error systems,that is,synchronization systems can get finite-time convergence which converge to the given sliding mode surface and remain on it forever.Numerical simulations verify that methods are better than that of relate studies.Thirdly,the problem of exponential synchronization of impulsive complex networks with time-varying delays and derivative coupling and the problem of exponential synchronization of impulsive complex networks with time-varying delays and distributed delay are studied,respectively.By designing linear feedback controllers and impulsive controllers,based on the contradiction method,some criteria for exponential synchronization are obtained,finally complex networks achieve exponential synchronization.And numerical simulations verify the effectiveness of the proposed schemes.Finally,the problem of a class of generalized exponential synchronization with time-varying delays and unknown parameters,based on Lyapunov functional stability theory,by designing a hybridcontrol with the adaptive feedback controllers and the updated laws of parameters,not only complex networks can achieve generalized exponential synchronization,but also in the process of generalized exponential synchronization,the parameters of networks can be identified.An example simulates the effectiveness of the results obtained.