On Successive Lag Synchronization of a Dynamical Network With Delayed Couplings

Kezan Li, Jie Zhao, Haifeng Zhang, Xiang Li

Abstract: Successive lag synchronization (SLS), an important synchronization phenomenon in nature and engineering, receives little attention in stability theory. In this article, we first propose a dynamical network model to realize the SLS with diffusive and delayed couplings, where the state of each node depends on the historical states of its neighbors. We give a series of stable conditions to achieve the local stability and global stability of the SLS manifold, and address the influence of network structure to guarantee the SLS. We find that the existence of a directed spanning tree of the network structure is the necessary condition for achieving the SLS, and design a novel algorithm to regulate the network structure to reach the SLS as well. Extensive examples illustrate the SLS performance with both the Lorenz systems and Chua's circuits embedded.