Synchronization of networks with time-varying couplings

In this paper,we present a review of our recent works on complete synchronization analyses of networks of the coupled dynamical systems with time-varying couplings.The main approach is composed of algebraic graph theory and dynamic system method.More precisely,the Hajnal diameter of matrix sequence plays a key role in investigating synchronization dynamics and the joint graph across time periods possessing spanning tree is a doorsill for time-varying topologies to reach synchronization.These techniques with proper modifcation count for diverse models of networks of the coupled systems,including discrete-time and continuous-time models,linear and nonlinear models,deterministic and stochastic time-variations.Alternatively,transverse stability analysis of general time-varying dynamic systems can be employed for synchronization study as a special case and proved to be equivalent to Hajnal diameter.