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Impulsive Destabilization Effect on Novel Existence of Solution and Global μ -Stability for MNNs in Quaternion Field

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  • Qingchao Meng

    (College of Artificial Intelligence, Southwest University, Chongqing 400715, China
    School of Information Technology (School of Software), Luoyang Normal University, Luoyang 471022, China)

  • Huamin Wang

    (College of Artificial Intelligence, Southwest University, Chongqing 400715, China
    School of Mathematics, Luoyang Normal University, Luoyang 471022, China)

Abstract

In this paper, a novel memristor-based non-delay Hopfield neural network with impulsive effects is designed in a quaternion field. Some special inequalities, differential inclusion, Hamilton rules and impulsive system theories are utilized in this manuscript to investigate potential solutions and obtain some sufficient criteria. In addition, through choosing proper μ ( t ) and impulsive points, the global μ -stability of the solution is discussed and some sufficient criteria are presented by special technologies. Then, from the obtained sufficient criteria of global μ -stability, other stability criteria including exponential stability and power stability can be easily derived. Finally, one numerical example is given to illustrate the feasibility and validity of the derived conclusions.

Suggested Citation

  • Qingchao Meng & Huamin Wang, 2023. "Impulsive Destabilization Effect on Novel Existence of Solution and Global μ -Stability for MNNs in Quaternion Field," Mathematics, MDPI, vol. 11(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1869-:d:1123737
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    References listed on IDEAS

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    1. Wang, Huamin & Wei, Guoliang & Wen, Shiping & Huang, Tingwen, 2021. "Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    3. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    4. Wang, Shengbo & Cao, Yanyi & Huang, Tingwen & Wen, Shiping, 2019. "Passivity and passification of memristive neural networks with leakage term and time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 294-310.
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