Synchronization Of Complex Dynamic Network With Time Delay On Time Scales

In recent years,complex dynamic networks(CDNs)have attracted more and more attention from researchers.Complex dynamic networks are not only involved in physics,mathematics,engineering,biology and social sciences,but also have been applied to real life.Researchers in various fields analyze the synchronization behavior of networks by building complex dynamic network models.At present,although the synchronization analysis of CDNs has achieved lots of results.But it is important to note that the universal existence of time delay in real life will inevitably impact on the network synchronization.Therefore,we propose the time scale theory to characterize the synchronization of complex dynamic networks with time delays.Besides,this paper focuses on the synchronization behavior of time-delay CDNs on time scale(also known as time scale).The main work and innovation points are summarized as follows:1.We investigate the impulsive synchronisation of linear complex dynamical networks(CDNs)with time delay on time scales by the pinning impulsive control method.Using Lyapunov stability theory and time scale theory,the synchronization criterion of complex dynamic networks is derived by establishing a new impulse delay inequality on time scale.In the end,we give a numerical simulation to demonstrate the feasibility of the theoretical analysis.Our result not only extends the determination theorem of the previous literature,but also enriches the existing research results of linear CDNs with time delay.The modelling framework also enriches the models of continuous/discrete-time CDNs.2.We discuss exponential synchronization of nonlinear CDNs via intermittent pinning control on time scale through the intermittent impulsive control technique.We use Lyapunov method,LMI and time scale calculation criterion to derive the sufficient conditions of the network synchronization.Specially,we also consider the two cases of integral delay and coupled disturbance in the original nonlinear CDNs,and the established model is not only suitable for continuous/discrete CDNs,but also for mixed CDNs.Therefore,our result is not only a generalization of the original result,but also a more complete proof.Finally,we give a numerical simulation to demonstrate the feasibility of our theory.