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Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps

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  • Tan, Jianguo
  • Tan, Yahua
  • Guo, Yongfeng
  • Feng, Jianfeng

Abstract

In this paper, we main investigate the almost sure exponential stability of stochastic delay Hopfield neural networks with jumps on numerical solutions. The methods we used are Euler approach and backward Euler approach. By giving some conditions of theoretical significance, we verify that not only Euler approach but also backward Euler approach is almost sure exponential stability. However, the range of application of Euler approach is smaller than that of backward Euler approach. Moreover, our main research tool is the discrete semimartingale convergence theorem. Lastly, we give an example as illustration.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321065
    DOI: 10.1016/j.physa.2019.123782
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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. Hongyu Qin & Zhiyong Wang & Fumin Zhu & Jinming Wen, 2018. "Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-5, June.
    3. 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.
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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. 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).

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