Almost periodic dynamics of fractional-order stochastic Hopfield neural networks with time-varying delays

Binrong Peng; Yongkun Li; Binrong Peng; Yongkun Li

doi:10.3934/math.2025823

AIMS Mathematics

2025, Volume 10, Issue 8: 18431-18453. doi: 10.3934/math.2025823

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Research article

Almost periodic dynamics of fractional-order stochastic Hopfield neural networks with time-varying delays

Binrong Peng ,
Yongkun Li ^,

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received: 08 June 2025 Revised: 02 August 2025 Accepted: 11 August 2025 Published: 14 August 2025
MSC : 34K14, 34K37, 92B20

Although fractional-order stochastic neural networks exhibit rich dynamics, there are currently no research results on their almost periodic dynamics in the sense of distribution. This paper investigated a class of fractional-order stochastic Hopfield neural networks with time-varying delays. By employing the Banach fixed point theorem and inequality techniques, we first established sufficient criteria for the existence and uniqueness of almost periodic solutions in distribution for the considered model. Subsequently, through the application of a generalized Gronwall inequality, the finite-time stability in the mean square sense of this unique almost periodic solution in distribution was rigorously demonstrated. The results obtained in this study are entirely novel. To validate the theoretical findings, a numerical example with explicit parameters was constructed for simulation verification, where computational results exhibit a high degree of consistency with theoretical derivations.
- fractional-order stochastic Hopfield neural networks,
- almost periodic solution in distribution,
- finite-time stability
Citation: Binrong Peng, Yongkun Li. Almost periodic dynamics of fractional-order stochastic Hopfield neural networks with time-varying delays[J]. AIMS Mathematics, 2025, 10(8): 18431-18453. doi: 10.3934/math.2025823

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Abstract

Although fractional-order stochastic neural networks exhibit rich dynamics, there are currently no research results on their almost periodic dynamics in the sense of distribution. This paper investigated a class of fractional-order stochastic Hopfield neural networks with time-varying delays. By employing the Banach fixed point theorem and inequality techniques, we first established sufficient criteria for the existence and uniqueness of almost periodic solutions in distribution for the considered model. Subsequently, through the application of a generalized Gronwall inequality, the finite-time stability in the mean square sense of this unique almost periodic solution in distribution was rigorously demonstrated. The results obtained in this study are entirely novel. To validate the theoretical findings, a numerical example with explicit parameters was constructed for simulation verification, where computational results exhibit a high degree of consistency with theoretical derivations.

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