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Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method

Author

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  • Jie Pan

    (Department of Applied Mathematics, Sichuan Agricultural University, Chengdu 611130, China)

  • Lianglin Xiong

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

Abstract

In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural networks (QNNs). The existence and uniqueness of the equilibrium solution (ES) for MQNN are concluded by exploiting the fixed-point theorem. Then a derivative formula of the quaternionic function’s norm is received. By utilizing the formula, the M -matrix theory, and the inequality techniques, some algebraic standards are gained to affirm the global exponential stability (GES) of the ES for the MQNN. Notably, compared to the existing work on QNN, our direct quaternionic method operates QNN as a whole and markedly reduces computing complexity and the gained results are more apt to be verified. The two numerical simulation instances are provided to evidence the merits of the theoretical results.

Suggested Citation

  • Jie Pan & Lianglin Xiong, 2021. "Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method," Mathematics, MDPI, vol. 9(11), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1291-:d:568838
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    References listed on IDEAS

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    1. M. Syed Ali & S. Saravanan & Quanxin Zhu, 2017. "Finite-time stability of neutral-type neural networks with random time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(15), pages 3279-3295, November.
    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. Guo, Runan & Zhang, Ziye & Liu, Xiaoping & Lin, Chong, 2017. "Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 100-117.
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