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

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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.

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Authors and Affiliations

  1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362000, China

    Jinsen Zhuang & Yan Zhou

  2. Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Jinsen Zhuang

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Yonghui Xia

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  1. Jinsen Zhuang
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  2. Yan Zhou
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  3. Yonghui Xia
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Correspondence to Yonghui Xia.

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This work was jointly supported by the National Natural Science Foundation of China under Grant (Nos. 11931016, 11671176, 11871231), Natural Science Foundation of Zhejiang Province under Grant (No. LY20A010016), Program for Innovative Research Team in Science and Technology in Fujian Province University, and Quanzhou High-Level Talents Support Plan under Grant 2017ZT012, start-up fund of Huaqiao University (Z16J0039).

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Zhuang, J., Zhou, Y. & Xia, Y. Intra-layer Synchronization in Duplex Networks with Time-Varying Delays and Stochastic Perturbations Under Impulsive Control. Neural Process Lett 52, 785–804 (2020). https://doi.org/10.1007/s11063-020-10281-0

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