Research Of Cluster Synchronization For Complex Dynamical Network Systems

As a special kind of differential dynamic systems,complex dynamic networks(CDNs)are a research hot spot in the science of nonlinear systems.With the deepening of research,people discover that complex networks are closely related to many aspects of nature and human society,so it begins to receive extensive attention from researchers in different fields.In particular,as one of the important dynamic behaviors of complex network systems,synchronous control is widely used in physics,engineering,computer science and other fields.In this paper,for different types of complex network systems,based on Lyapunov stability theory and advanced mathematical analysis methods,several global synchronization problems for CDNs are studied.The main research contents are as follows:Firstly,based on the aperiodic intermittent control(AIC)method,we mainly study the global cluster synchronization in finite time for CDNs with hybrid couplings.Under the designed controller,the upper bound of settling time is estimated accurately.Moreover,the correctness and feasibility of the theoretical results are verified through numerical simulations.Secondly,according to the stochastic analysis theory,the lemma of global fixed-time convergence for stochastic switching system is proposed.By employing the differential inclusion theory,the fixed-time cluster synchronization for semi-Markovian switching CDNs with discontinuous dynamic nodes is discussed.Furthermore,the upper bound of fixed settling-time is accurately estimated.With the help of random Lyapunov-Krasovskii functional method,the sufficiency synchronization conditions in the form of linear matrix inequalities(LMIs)are established.Finally,on the basis of the related definitions of mode-dependent average impulsive interva(MDAII)and mode-dependent average dwell time(MDADT),using multiple Lyapunov function methods,inequality analysis techniques and pinning control strategies,the global pinning cluster synchronization for fractional-order CDNs with switching topologies is studied.