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Synchronization of drive-response networks with event-based pinning control

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Abstract

This work investigates the pinning synchronization problem of a drive-response network with nonlinear nodal dynamics under dynamic pinning strategy, where the control signal updates according to some well-designed triggering condition so as to reduce the control cost. By using a novel differential inequality, sufficient criteria are derived to guarantee synchronization, revealing the crucial role of the time average of the smallest eigenvalue of an augmented matrix in spite of the changeable pinning strength. Meanwhile, Zeno phenomenon is also successfully excluded. As applications, the main theorem is utilized to examine some specified dynamic pinning strategies, such as pinning control with periodic intermittency, switching pinned node set, and nonlinear pinning strength. An interesting finding is that drive-response synchronization is possible even when the underlying topology is disconnected. Finally, numerical examples on coupled Hopfield neural networks and networked nonlinear oscillators are given for demonstration purpose.

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu University, Zhenjiang, China

    Qiang Jia & Andrew K. Bram

  2. Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong

    Zeyu Han

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  1. Qiang Jia
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  2. Andrew K. Bram
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  3. Zeyu Han
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Correspondence to Qiang Jia.

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Jia, Q., Bram, A.K. & Han, Z. Synchronization of drive-response networks with event-based pinning control. Neural Comput & Applic 33, 8649–8658 (2021). https://doi.org/10.1007/s00521-020-05619-7

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  • DOI: https://doi.org/10.1007/s00521-020-05619-7

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