Research On Synchronization Of Some Dynamical Networks With Mixed Coupling And Time Delay

A complex network consists usually of a large set of coupled interconnected nodes,in which each node is a fundamental unit with detailed contents.Complex networks have drawn much interest from researchers in different areas,such as mathematics,physics,biology,engineering,society sciences,and so on.The spatio-temporal evolution of complex dynamical networks can exhibit various complex dynamical behaviors.Particularly,the synchronization of all dynamical nodes in complex dynamical networks is a universal and important phenomenon.In science and technology,synchronization is considered as time coherence of different process.Synchronization has been the hot topic in the study of complex networks in recent years,and a great number of results on this topic have been reported in the literature.In addition,time delays occur commonly in complex networks due to the finite speeds of transmission as well as traffic congestions.Thus,it is important and practical to study the synchronization problem of complex networks with time delays.Based on the current research situation on the synchronization of complex dynamical networks,this dissertation addresses synchronization of several kinds of complex delayed dynamical networks with mixed coupling.The main content of this dissertation are summarized as follows:1)We investigate the pinning adaptive hybrid synchronization of two complex dynamical networks with mixed coupling.The Lyapunov stability theory,Barbalat lemma.Schur complement lemma and matrix decomposition method are employed to obtain some synchronization criteria less-conservative and easy to verify.Moreover,the hybrid synchronization problem is discussed for drive-response networks with mixed coupling,in which each network node is a delayed dynamical system with distributed delay.Numerical examples are given to demonstrate the effectiveness of the proposed synchronous criteria.2)We devote to studying the problem of hybrid synchronization for drive-response networks with nonidentical topologies and mixed coupling.Hybrid synchronization with nonidentical nodes and topologies is challenging work in drive-response networks.A kind of entrainment hybrid synchronization for two different networks is achieved via the open-loop-plus-pinning adaptive control strategy.The new hybrid synchronization scheme makes the outer synchronization analysis of network easier.3)We discuss the finite-time synchronization for complex dynamical networks with hybrid coupling and time-varying delay.Up to now,synchronization analysis of complex dynamical networks in most known results is defined over an infinite time interval.That is,the results related to synchronization are Lyapunov asymptotic.In many practical situations,however,the main concern is the finite-time synchronization of complex networks,in other words,the synchronization error remains within the prescribed bound in the fixed time interval.Based on Lyapunov-Krasovskii functional method and matrix decomposition method,and the concept of finite-time stability,this dissertation studies the finite-time synchronization of a complex network with mixed coupling and time-varying delay,and proposes some synchronization criteria less-conservative and delay-dependent.Numerical examples show the correctness of theoretical work.4)We mainly investigate the problem of finite-time outer synchronization for two complex networks with mixed coupling.Firstly,we give the definition of ordinary finite-time outer synchronization between two networks.Secondly,some sufficient conditions of ordinary finite-time outer synchronization are derived for two general complex dynamical networks with mixed coupling and time-varying delay by the pinning control strategy.Finally,we discuss the ordinary finite-time outer synchronization of drive-response networks with different time-varying delays.