Research On Synchronization Of Several Kinds Of Complex Network Dynamic Systems

Since the last half of the 20 th Century,with the rapid development of information technology,the human society entered the era of network.Network has prevailed over all areas of our lives,such as Internet,World Wide Web(WWW),communication networks,social networks,gene regulatory networks and television networks.Nowadays,we has lived in all kinds of complex networks(CN)in the world.This phenomenon sets off a boom of research on CS theory,attracted researchers in various fields of physics,mathematics,engineering,communication,biology to study the nature of the complex world,so that the CS have become a hot issue in the research of many fields.Synchronization and control of complex network dynamic system(CNDS)are an important part of the research and application of CS,the research of nonlinear dynamics is effective theoretical foundation and tool to investigate synchronization,and synchronization has been applied potentially to the network congestion control,harmonic oscillator generation,multi-agent consensus and so on.In this paper,synchronization and control of CNDS are studied,some network models are considered,such as time-varying delay(TVD)CN,delay coupling CN,asymmetric coupling CN and so on.Based on Lyapunov stability theory,matrix theory and control theory,combined with pinning control method(PCM),the synchronization of CNDS is studied to achieve some criterion of complete synchronization,cluster synchronization(CS)and function projective synchronization(FPS).Matlab numerical simulations are given to illustrate the effectiveness of the obtained results.The following is the main research works in this paper:1.The synchronization problem of CNDS with delay and asymmetric coupling matrix is studied.By constructing effective Lyapunov functionals and splitting the asymmetric matrix into two matrices which are deal with by different methods,and the sufficient conditions are obtained for the synchronization of CNDS.2.The synchronization of CNDS with TDV is studied.TDV usually leads to instability and shock of power systems,even system performance is reduced.Therefore,in this paper,an adaptive controller is developed to control the complex system to achieve synchronization.3.The CS of CNDS with delay and non-delay linear coupling matrix is studied.The controller is used to control a part of nodes,so that the whole network can achieve synchronization.The delayed and non-delayed linear coupling term are considered in the network system.The system can obtain synchronization via linear feedback pinning control and adaptive pinning control,respectively.4.The FPS of CNDS with asymmetric coupling is studied.By constructing Lyapunov functional,splitting asymmetric matrix into three kinds of matrices which are dealed with different methods respectively,and designing adaptive controller and pinning controller,FPS of CNDS is obtained.5.The synchronization problem of SCNDS with TVD is studied.By constructing effective Lyapunov functionals,using the segmentation method of TVD,and designing pinning feedback controller,the SCNDS model can achieve synchronization.