General decay synchronization of complex multi-links time-varying dynamic network

In this paper, we discuss the decay synchronization of complex multi-links time-varying dynamic networks (CMTDNs) for the first time. The exponential synchronization, polynomial synchronization and logarithmic synchronization can be seen as the special cases of the decay synchronization. CMTDNs are more general and realistic than the complex network with the single-link. By virtue of the definitions of the ψ-type function and ψ-type stability, we give the definition of the decay synchronization of the drive-response CMTDNs. Some novel and easily validated sufficient conditions are deduced to ensure the decay synchronization of drive-response CMTDNs based on the Lyapunov stability theory with the help of a novel nonlinear feedback controller and a new Lyapunov-Krasovskii function. Finally, two numerical simulations have been given to verify the correctness of main results.