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Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks

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  • Rathinasamy, A.
  • Narayanasamy, J.

Abstract

In this paper, the two-step Maruyama methods of stochastic delay Hopfield neural networks are studied. We have found that under what choices of step-size, the two-step Maruyama methods of stochastic delay Hopfield networks, maintain the stability of exact solutions. The mean-square stability of two-step Maruyama methods of stochastic delay Hopfield neural networks is investigated under suitable conditions. Also, the almost sure exponential stability of two-step Maruyama methods of stochastic delay Hopfield networks is proved using the semi-martingale convergence theorem. Further, the comparisons of stability conditions to the previous results in Liu and Zhu (2015), Rathinasamy (2012) and Ronghua et al. (2010) are given. Numerical experiments are provided to illustrate our theoretical results.

Suggested Citation

  • Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:126-152
    DOI: 10.1016/j.amc.2018.11.063
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    References listed on IDEAS

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    1. 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.
    2. Li, Xiuping & Cao, Wanrong, 2015. "On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 373-381.
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    Cited by:

    1. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Yu, Peilin & Deng, Feiqi & Sun, Yuanyuan & Wan, Fangzhe, 2022. "Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    4. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    5. Wang, Fen & Chen, Yuanlong, 2021. "Mean square exponential stability for stochastic memristor-based neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Li, Zhao-Yan & Shang, Shengnan & Lam, James, 2019. "On stability of neutral-type linear stochastic time-delay systems with three different delays," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 147-166.
    7. Tan, Jianguo & Tan, Yahua & Guo, Yongfeng & Feng, Jianfeng, 2020. "Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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