Intra-layer Synchronization in a Duplex Networks with Noise
• Jinsen Zhuang,
• Yan Zhou,
• Yonghui Xia
Jinsen Zhuang
Huaqiao University

Corresponding Author:zzjinsen@hqu.edu.cn

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Yan Zhou
Huaqiao University
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Yonghui Xia
zhejiang Normal University
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## Abstract

This paper concerns the impact of stochastic perturbations on the intra-layer synchronization of the duplex networks. A duplex network contains two layers ([1,2]). Different from the previous works, environmental noise is introduced into the dynamical system of the duplex network. We incorporate both the inter-layer delay and the intra-layer delay into the dynamical system. Both of the delays are time-varying. However, the paper [1] only considered the intra-layer delays and they are assumed as the constants. While the paper [2] did not consider the inter-layer delay or intra-layer delay. When the system does not achieve automatic intra-layer synchronization, we introduce two controllers: one is the state-feedback controller, the other is the adaptive state-feedback controller. Interestingly, we find that the intra-layer synchronization will achieve automatically if the inter-layer coupling strength $c_1$ is large enough when the time-varying inter-layer delays are absent. Finally, some interesting simulation results are obtained for the Chua-Chua chaotic system with application of our theoretic results, which show the feasibility effectiveness of our control schemes.
27 May 2021Submitted to Mathematical Methods in the Applied Sciences
28 May 2021Submission Checks Completed
28 May 2021Assigned to Editor
09 Jun 2021Reviewer(s) Assigned
25 Jun 2021Review(s) Completed, Editorial Evaluation Pending
15 Jul 2021Editorial Decision: Revise Major