Synchronization Of Several Classes Of Complex Networks On Time Scales

In recent years,complex networks have received great attention due to the widespread use of complex networks in many fields such as nature science,biology and computer science.In addition,the dynamic equations of time scales and corresponding applications have became a research hot spot in recent years with the establishment of time scales theory.The problem of synchronization and synchronization control is one of the most demonstrating topics in complex networks.It is more general to investigate complex networks via the theory of time scales.The dynamical system on time scales not only describes the continuous or discrete cases,but also describes the hybrid time domains.Therefore,it is of great practical significance and theoretical value to study the synchronization of complex networks on time scales.However,there are several types of synchronization have not been concerned yet,especially quasi-synchronization and cluster synchronization.On the basis of the existing results and the theory of time scales,exponential synchronization,quasi-synchronization and cluster synchronization issues are studied in this paper.Based on the theory of time scales,synchronization problems of several kinds of complex networks models have been analyzed in this paper.In the first part,the exponential synchronization of Wilson-Cowan networks with constant time delay on time scales is discussed.The criteria for global exponential synchronization of networks is established by constructing the theory of time scales,Lyapunov functions and using linear matrix inequalities.In the second part,we consider the quasi-synchronization issue of complex networks with parameter mismatches on time scales.We design an impulsive controller that takes into account of time delay and the error range of the network to achieve quasi-synchronization is given by using the theory of impulsive differential equation.In the third part,the cluster synchronization for directed network of partial-state coupled linear system is solved and we obtain the conditions of synchronization under fixed topology and switching topology,respectively.Finally,numerical simulations are given to verify the validity of the obtained conclusion.