Synchronization And Local Convergence Analysis Of Complex Dynamical Networks With Time Delay

In recent years,the coordination and group behaviors of complex networks have received more and more attention since they have a wide range of roles in the fields of physics,biology,and engineering.The synchronization of complex networks means that the state of all nodes is consistent with that of the target nodes over time.Synchronization is common seen in complex networks and is a the most common dynamic behavior.As a consequence,the study of the synchronization of complex networks can provide new ideas and methods for many complex systems in reality.Therefore,the research on the synchronization of complex networks is important both theoretically and practically in significance.In real networks,due to the limited transmission of signals,there are inevitable time delay in the system.When solving practical problems,in order to make the established model more realistic,the impact of time delay on the system must be considered.Therefore,it is very important to study complex networks with time delays.This paper mainly studies the problem of local stability for two kinds of complex networks with constant time delays.And using Lyapunov stability theory and nonlinear theory method and other technologies,local synchronization and local exponential synchronization of these two types of complex networks are obtained.In the sense of the given error systems and synchronous manifolds,chapter three and chapter four respectively study the local synchronization and local exponential synchronization of complex networks with nodes delays as well as complex networks with double-delays.Based on the theory of Lyapunov stability,this paper presents the sufficient conditions of local synchronization and local exponential synchronization for these two types of systems.Furthermore,these two conditions are proved by the direct method of Lyapunov and the validity of the results is verified by numerical experiments.