Stochastic Outer Synchronization Of Complex Dynamical Networks

Ranging from molecular movements in human cells to political and economic relations among different countries,many systems in our real life can be analyzed with complex networks.Nowadays,the research on complex networks has become a hot topic,especially in social networks,computer networks,ecological networks and so on.For example,sociologists use complex networks to study the relationships between people;computer scientists use complex networks to map the structure of the Internet and the World Wide Web;biologists use complex networks to study signal transduction and metabolic processes of biological cells.In the study on dynamic behavior of complex networks,the synchronization prob-lem has very important practical significance.Network synchronization refers to the phenomenon that the dynamic states of nodes tend to be consistent through the in-teraction between systems under different initial conditions.Noise is ubiquitous in many natural and man-made systems.Therefore,it is necessary to investigate the ef-fect of noise on network synchronization.Noise coupling is often regarded as random and continuous interference to the system,which may cause the transmission signal to be blocked or weakened.However,researchers have found that noise perturbation in complex networks may also improve the stability of the networks,such as changing the unstable state into a stable state,or making the original stable state more stable.This dissertation mainly studies the stochastic outer synchronization of complex dynamics networks.Based on the stability theory of stochastic differential equations and the properties of matrix inequalities,we focus on the stochastic lag outer synchro-nization of complex networks,stochastic outer synchronization of uncertain complex networks with time-delay,stochastic outer synchronization of complex networks with partial delay,and the fixed-time stochastic outer synchronization of complex networks.Sufficient conditions for achieving stochastic outer synchronization are obtained.The main work are as follows:1.The stochastic lag outer synchronization of complex networks is investigated.We use linear controllers with noise coupling to analyze the outer synchronization of complex networks.Sufficient conditions for stochastic lag outer synchronization are obtained.The theoretical analysis and numerical simulations show that lag outer syn-chronization can be achieved under the controllers with noise perturbation even if the outer coupling matrix is asymmetric or reducible.2.The stochastic outer synchronization for uncertain complex networks with time-delay is discussed.An uncertain complex network with time-delay and noise coupling is constructed.Based on the LaSalle invariance principle of stochastic delay differential equation,the outer synchronization of complex networks with noise cou-pling is analyzed via adaptive controllers.Sufficient conditions for achieving stochastic outer synchronization are given.Finally,the effect of adaptive control parameters is in-vestigated.3.The stochastic outer synchronization of complex networks with partial delay is studied.We construct a complex network model with partial delay and noise cou-pling,and obtain sufficient conditions for stochastic outer synchronization via adaptive pinning control.The validity of the theoretical analysis is verified by numerical simu-lations,and the effect of noise and the percentage of pinning nodes is analyzed.4.The fixed-time stochastic outer synchronization of complex networks with noise coupling is studied.To ensure that the setting time of synchronization is not affected by the initial states,based on the fixed-time stability theory of stochastic dif-ferential equation,a novel fixed-time synchronization controller is proposed.Sufficient conditions for fixed-time synchronization of complex networks with noise coupling are obtained,and the upper bound of setting time is estimated.