Stability of stochastic delay Hopfield neural network with Poisson jumps

Hongjie Xu, Huantian Luo and Xu-Qian Fan

Chaos, Solitons & Fractals, 2024, vol. 187, issue C

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.

Keywords: Hopfield neural network; Poisson jumps; Time-varying delays; Stability; Euler scheme (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009561

DOI: 10.1016/j.chaos.2024.115404

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