Successive lag synchronization of a complex network with noise via aperiodically intermittent pinning control

Abstract

Successive lag synchronization (SLS) is a novel and important synchronization pattern, whose control problem has been deeply investigated in the past several years. However, the impact of noise perturbation on the control of SLS is still unclear. To this end, this paper focuses on the intermittent pinning control of SLS on a dynamical network with noise perturbation. In order to push the SLS to a desired trajectory, we design an intermittent pinning control scheme that is active only on controlled intervals and a small proportion of nodes. By applying the stability theory of stochastic differential equation, we obtain sufficient conditions under which the network can realize the SLS with exponential stability in mean square. According to these conditions, we can determine which nodes should be controlled or not, the minimum control ratio and the impact of noise perturbation on the SLS. An interesting finding is that performing the control on at least half of each subinterval can ensure the stochastic stability of SLS, which is independent of any network parameters. The effectiveness of proposed intermittent pinning control scheme is verified by the network of coupled Chua’s circuits.