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Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures

Author

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  • Zhifu Jia

    (School of Sciences and Arts, Suqian University, Suqian 223800, China
    These authors contributed equally to this work.)

  • Cunlin Li

    (Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Governance and Social Management Research Center of Northwest Ethnic Regions, North Minzu University, Yinchuan 750021, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China
    These authors contributed equally to this work.)

Abstract

For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, we deduce two corollaries, using the Itô–Liu formula. Then, we introduce the concept of almost sure exponential stability for uncertain stochastic Hopfield neural networks. Next, we investigate the almost sure exponential stability of uncertain stochastic Hopfield neural networks, using the Lyapunov method, Liu inequality, the Liu lemma, and exponential martingale inequality. In addition, we prove two sufficient conditions for almost sure exponential stability. Furthermore, we consider stabilization with linear uncertain stochastic perturbation and present some exceptional examples. Finally, our paper provides our conclusion.

Suggested Citation

  • Zhifu Jia & Cunlin Li, 2023. "Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3110-:d:1194101
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    References listed on IDEAS

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    1. Wang, Zidong & Lauria, Stanislao & Fang, Jian’an & Liu, Xiaohui, 2007. "Exponential stability of uncertain stochastic neural networks with mixed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 62-72.
    2. Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
    3. Weiyin Fei, 2014. "Optimal control of uncertain stochastic systems with Markovian switching and its applications to portfolio decisions," Papers 1401.2531, arXiv.org.
    4. Wang, Zidong & Fang, Jian’an & Liu, Xiaohui, 2008. "Global stability of stochastic high-order neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 388-396.
    5. Lu, Jun-Xiang & Ma, Yichen, 2008. "Mean square exponential stability and periodic solutions of stochastic delay cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1323-1331.
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    Cited by:

    1. Zhifu Jia & Cunlin Li, 2024. "Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures," Mathematics, MDPI, vol. 12(8), pages 1-15, April.
    2. Wei Ouyang & Kui Mei, 2023. "Quantitative Stability of Optimization Problems with Stochastic Constraints," Mathematics, MDPI, vol. 11(18), pages 1-13, September.

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