Synchronization Of Complex-valued Complex Networks With Time Delays Via Delayed Impulsive Control

Signal in transmission is inevitably affected by external factors,which can greatly damage the realization of chaos synchronization.Hence,this paper focuses on the syn-chronization and control of complex dynamical networks(CDNs)with coupling delays in the following three cases:(a)CDNs with nonlinear interference and discontinuous activation functions;(b)complex-valued complex dynamical networks(CVCDNs)with nonidentical discontinuous nodes;(c)CVCDNs with time-varying delays and stochastic perturbations.First,based on the concept of Filippov solutions,differential inclusion,and nons-mooth analysis,globally exponential synchronization of CDNs with nonlinear interference and discontinuous activation functions via time-delayed impulsive control and feedback control is investigated.By designing suitable time-delayed impulsive control and feed-back control,sufficient conditions for globally exponential synchronization are obtained through rigorous mathematical proofs.Results of this paper are general and include the results that for CDNs with continuous activations as a special case.Numerical simulations verify the effectiveness of the theoretical results.Second,the problem of finite-time synchronization of CVCDNs with nonidentical discontinuous nodes via feedback control is investigated.In order to overcome the effects of the difference among the nonidentical dynamical nodes and couple delays,by designing a simple feedback control,the CVCDN can be synchronized to an isolated node.Based on Lyapunov stability theorem,Filippov solutions and differential inclusion,sufficient conditions for finite-time synchronization are obtained through rigorous mathematical proofs.Numerical simulations verify the effectiveness of the theoretical results.Finally,the problem of globally exponential synchronization of CVCDNs with time-varying delays and stochastic perturbations via time-delayed impulsive control is investi-gated.By designing a time-delayed impulsive control,the CVCDN can be synchronized onto an isolated node.Based on Lyapunov stability theorem and differential inequality,sufficient conditions for globally exponential synchronization are obtained through rigor-ous mathematical proofs.Numerical simulations verify the effectiveness of the theoretical results.