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Exponential stability of periodic solution for a memristor-based inertial neural network with time delays

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Abstract

In this paper, exponential stability of periodic solution for an inertial neural network is studied. Different from most research on inertial neural networks, the model in this paper is based on memristors and is involved with periodic solutions. In order to simplify the difficulty in dealing with inertial terms and constructing Lyapunov functions, the inertial neural network in this paper is transformed into a suitable neural network with enhanced characteristics by using appropriate variable transformation method. Under the Lyapunov stability theory and Leary-Schauder alternative theorem, we prove the existence and global exponential stability of the periodic solution for the inertial neural network under mild conditions. At last, the feasibility of the theoretical conclusions is illustrated by some numerical examples.

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Acknowledgements

This research is supported by the National Science Foundation of China (61773136, 11471088).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, People’s Republic of China

    Sitian Qin, Liyuan Gu & Xinyu Pan

Authors
  1. Sitian Qin
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  2. Liyuan Gu
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  3. Xinyu Pan
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Correspondence to Sitian Qin.

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Conflict of interest statement

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Exponential Stability of Periodic Solution for a Memristor-based Inertial Neural Network with Time Delays.”

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Qin, S., Gu, L. & Pan, X. Exponential stability of periodic solution for a memristor-based inertial neural network with time delays. Neural Comput & Applic 32, 3265–3281 (2020). https://doi.org/10.1007/s00521-018-3702-z

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  • DOI: https://doi.org/10.1007/s00521-018-3702-z

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