Input-to-state stability of stochastic functional reaction–diffusion neural networks with Lévy noise and infinite delay

Weisong Zhou, Yinjian Shen and Zhichun Yang

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: Our paper focus on the input-to-state stability (ISS) of the reaction–diffusion system driven by Lévy noise and infinite delay. With the interference of distributed and boundary inputs, it is preferred via the newly developed Lyapunov method rather than the fixed point method to tackle our designed system. Taking the norm of infinite delay into account, the sufficient conditions of mean-square exponential (or integral) ISS are established. Moreover, combined with Chebyshev’s inequality, the adequate criteria ensuring the stochastic exponential (or integral) ISS are obtained. By means of numerical simulation, our examples are given to show the effectiveness.

Keywords: Exponential input-to-state stability; Integral input-to-state stability; Reaction–diffusion neural networks; Lévy noise; Infinite delay (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012007

DOI: 10.1016/j.chaos.2025.117187

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