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Stability of stochastic delay Hopfield neural network with Poisson jumps

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  • Xu, Hongjie
  • Luo, Huantian
  • Fan, Xu-Qian

Abstract

This paper focuses on the stochastic Hopfield neural networks perturbed by Poisson jumps with multiple time-varying delays. We first study the almost sure exponential stability and the pth moment exponential stability of the analytical solutions to the system, leveraging the semi-martingale convergence theorem. Subsequently, we introduce the Euler numerical solution for the model and prove that the Euler method converges with order 0.5 in the mean square sense. Furthermore, we demonstrate that under certain conditions, the Euler method exhibits mean square stability. Finally, we provide two examples to validate our results.

Suggested Citation

  • Xu, Hongjie & Luo, Huantian & Fan, Xu-Qian, 2024. "Stability of stochastic delay Hopfield neural network with Poisson jumps," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009561
    DOI: 10.1016/j.chaos.2024.115404
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    References listed on IDEAS

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    1. 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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    8. 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).
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