Synchronization Of Heterogeneous Complex Dynamic Networks

Complex networks have attracted the attention of scholars in multiple disciplines due to their wide application and interdisciplinary characteristics.Synchronization control of complex networks is an important research topic in dynamics research of complex networks.Most of the existing research results are based on homogeneous complex networks,however,the heterogeneous complex networks are ubiquitous due to dynamic diversities and parametric uncertainties.This thesis analyzes synchronization of several kinds of heterogeneous complex networks.Specifically,this thesis studies synchronization of heterogeneous networks coupled by LC oscillators,synchronization of heterogeneous complex networks under communication constraints,and synchronization of multilayer heterogeneous complex networks with a leader of unknown external input.The main results are as follows:(1)The complex dynamical networks coupled by heterogeneous LC oscillators are analyzed,and quasi-synchronization of the heterogeneous networks is realized by designing a sampling control protocol.The sufficient criteria for quasi-synchronization are derived based on the delayed input method and Lyapunov stability theory.Furthermore,the upper bound of quasisynchronization errors is estimated.(2)Synchronization of heterogeneous complex dynamical networks with input saturation and quantization limitations is discussed.By introducing a leader and designing the controller involved the quantization and actuator saturation,the heterogeneous dynamical networks can be transformed into the corresponding error systems with bounded disturbances.A sufficient criterion ensuring the error system can be exponentially stable and convergent to a bounded region is established via the Lyapunov functional approach.Based on the criterion,the control gain matrix is further designed to facilitate the design of the controller.(3)The pinning quasi-synchronization problem of multilayer heterogeneous complex networks is studied.Firstly,a class of heterogeneous complex network model with a two-layer topology is proposed,in which both the dynamics of the network nodes and the topologies of the two layers are heterogeneous.Additionally,the leader has nonzero control inputs that have unknown states and are unavailable to the followers.Secondly,two discontinuous coupling laws,corresponding to the static coupling and adaptive coupling,are designed to achieve quasisynchronization of multilayer heterogeneous networks by means of pinning control.Then,based on the Lyapunov stability theory and the matrix theory,several sufficient criteria for pinning quasisynchronization are derived.Finally,the upper bound of quasi-synchronization errors is estimated,and the relationship between the error convergence rate and the coupling strength is given by numerical simulations.