Research On Synchronization Problem Of Complex Dynamical Networks On Time Scales

Complex dynamical networks have been used to describe many problems in the real world.At present,many scholars have studied synchronization of complex dynamical networks in-depth.But most of researchers have discussed the synchronization of continuoustime and discrete-time complex dynamical networks separately.However,in many practical problems,the time domain is mixed,which includes both some continuous-time intervals and some discrete-time moments.In order to study the synchronization problem of complex dynamical networks on general time domain,we are concerned with the synchronization problem of complex dynamical networks on time scales in this thesis.Based on the time scales theory and Lyapunov method,the synchronization problem of complex dynamical networks on time scales is studied deeply and systematically.The main work includes the following aspects:(1)Research on self-synchronized complex dynamical networks on time scalesFirstly,based on the definition of complete synchronization of continuous-time complex dynamical networks,the definition of complete synchronization of complex dynamical networks on time scales is given.Secondly,we study the synchronized state when a given complex dynamical network on time scales is self-synchronized.Thirdly,some sufficient conditions for the self-synchronized complex dynamical networks on time scales are established,which combine the nonlinear function,the coupled strength,the coupled configuration matrix,the inner-coupled matrix or the nonlinear coupled function and the characteristics of the time scales.Finally,two numerical examples are given to verify the results obtained.(2)Research on synchronization of linear coupled complex dynamical networks on time scales via feedback pinning controlIt is necessary to design appropriate controller to achieve the desired synchronization quickly and effectively when a given complex dynamical network is not self-synchronized or the synchronized state is not the desired one.We design the feedback pinning control to study the synchronization problem of linear coupled complex dynamical networks on time scales.The results show that the feedback pinning synchronization criteria of the linear coupled complex dynamical networks on time scales not only unify and generalize the feedback pinning synchronization criteria of continuous-time and discrete-time complex dynamical networks,but also give the feedback pinning synchronization criteria of the linear coupled complex dynamical networks on the mixed time domain.Meanwhile,some numerical simulation examples are also included to verify the results obtained.(3)Research on synchronization of linear coupled complex dynamical networks on time scales via periodic intermittent pinning controlIn order to reduce the control cost,we design the periodic intermittent pinning control strategy to investigate the synchronization problem of linear coupled complex dynamical networks on time scales.Compared with the continuous-time case,it is difficult to analyze the synchronization of linear coupled complex dynamical networks on time scales by periodic intermittent pinning control strategy.By constructing Lyapunov function,the synchronization of linear coupled complex dynamical networks on time scales via the periodic intermittent pinning control strategy is studied.Some sufficient conditions for the synchronization of linear coupled complex dynamical networks on time scales via periodic intermittent pinning control strategy are obtained.At the same time,a numerical simulation example is given to verify the effectiveness of theoretical results.(4)Research on synchronization of nonlinear coupled complex dynamical networks on time scales via feedback pinning controlIn some real-world,the coupled mechanism of networks model is nonlinear between node state components.Therefore,it is valuable to study the synchronization problem of nonlinear coupled complex dynamical networks.In order to realize the synchronization of nonlinear coupled complex dynamical networks on time scales,we design feedback pinning control strategy.By applying some appropriate conditions to the nonlinear function and the nonlinear coupled function of the networks,some sufficient conditions for the synchronization of nonlinear coupled complex dynamical networks on time scales via feedback pinning control are obtained.At the same time,some sufficient conditions for synchronization of complex dynamical networks on discrete-time domains via feedback pinning control are established.Moreover,some numerical examples are given to verify our results.The complex dynamical networks on time scales investigated in this thesis include not only continuous-time and discrete-time complex dynamical networks,but also complex dynamical networks on the general time domains,such as the complex dynamical networks on the mixed time domain.In addition,some pinning synchronization criteria for complex dynamical networks on the discrete-time domains are obtained.At the same time,our results have revealed the differences of the pinning synchronization between continuous-time and discrete-time complex dynamical networks.Therefore,the research of this thesis has important theoretical significance and practical application value.