Cluster Synchronization Of Discrete And Continuous Spatiotemporal Networks With Different Structure

Synchronization phenomenon is a very important dynamic behavior in complex networks and has a wide range of applications in practice.This thesis focuses on the cluster synchronization problem of complex networks with uncertain parameters.Firstly,the cluster synchronization of discrete time-space networks with different structures is researched;Secondly,the global control is transformed to the local control,and then local control technology is further used to achieve the synchronization between each cluster of node within continuous space-time network and the target system.The main works of this thesis include:In the first chapter,the development of complex network is briefly introduced,and the characteristic quantities describing complex networks and several typical complex networks are described.Finally,the research significance of complex network is stated.The second chapter introduces the research background of network synchronization and synchronization methods,and simply exposits the applications of network synchronization in practice.Because cluster synchronizations are main works in this thesis,the related knowledge of cluster synchronization is introduced at the end of this chapter.In the third chapter,the synchronization of discrete spatiotemporal networks with discrete structures is investigated.Based on Lyapunov stability theory,a reasonable Lyapunov function is designed and the synchronization of discrete spatiotemporal networks with discrete structures is realized,at the same time the update rules to determine the unknown parameters are also derived.In the part of numerical simulation,we select the state equation of laser phase conjugate wave space chaotic expansion system,Gibbs optical spatiotemporal chaos Bragg model,acousto optical spatiotemporal chaos model as the nodes of three cluster networks to verify the effectiveness of the synchronization principle through the simulations.The fourth chapter uses the local control technology to realize the cluster synchronization problem of continuous complex networks.By designing the proper Lyapunov function,the expression of the local controller is derived and the update rules of unknown parameters in the network can be obtained.The coupled-wave equations of stimulated Raman scattering with spatiotemporal chaos behavior and single-mode laser Maxwell-Bloch equations are selected as a cluster of state equations of network nodes and the corresponding target system,respectively.And then a series of simulations are completed to verify the general applicability of the principle.The fifth chapter makes a summary of the research contents of this thesis and makes a tentative plan for the future research work about the complex network.