Successive lag synchronization of nonlinear stochastic networks with arbitrary structure via pinning control

Abstract

In this article, a new nonlinear stochastic network with arbitrary structure and noise is proposed for realizing the successive lag synchronization (SLS).Both the constant and adaptive pinning control laws are designed respectively to regulate the SLS to desired chaotic states, where the network structure can be directed, weighted, time-varying and even not strongly connected. Several sufficient conditions for guaranteeing the stochastic asymptotic stability of SLS are derived by means of the Lyapunov stability theory. First, we demonstrate that the pinned nodes can be fixed via 1-dimensional inequalities, which explicitly provide how many nodes and which nodes should be controlled. Besides, those connections from a node with a given number to other nodes with smaller numbers will lead to the increase of pinned nodes. Second, our results indicate that, in order to make the SLS stable the coupling strength must belong to a bounded interval for both the pinning control schemes. Finally, we conclude that strong noise perturbation will lead to the increase of pinned nodes and even break the SLS. The theoretical results are validated with different numerical examples by embedding the chaotic Chua's circuit to each node.