Intra-layer Synchronization in Duplex Networks with Time-Varying Delays and Stochastic Perturbations Under Impulsive Control

Abstract

This paper concerns the intra-layer synchronization in duplex networks with stochastic perturbations under impulsive control. In this paper, we proposed a dynamical system on a duplex network with impulsive control, where delay of interactions within each layer, delay of interactions between layers, and environmental noises are included. Different from Tang et al. (Sci China Technol Sci 61(12):1907–1914, 2018), we used different topology structures for the two layers of the duplex network. Different from the model of Shen and Tang (Chin Phys B 27(10):100503, 2018), delays in the node interactions within or between the layers are allowed. Besides, the environmental noises are included. Moreover, due to the superior efficiency of impulsive control, we use it to control the synchronization of the duplex network even if the dynamical system exhibits chaos phenomena. Finally, we obtain some interesting simulation results by applying our theoretic results to the Chua–Chua chaotic system to show the effectiveness of our control schemes.