Random Attractors of a Stochastic Hopfield Neural Network Model with Delays

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-21 DOI:10.1007/s12346-024-01082-0

Wenjie Hu, Quanxin Zhu, Peter E. Kloeden, Yueliang Duan

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Abstract

The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is firstly proved that the trajectory field of the stochastic delayed HNNM admits an almost sure continuous version, which is compact for \(t>\tau \) (where \(\tau \) is the delay) by a construction based on the random semiflow generated by the diffusion term due to Mohammed ( Stoch. Stoch. Rep. 29: 89–131, 1990). Then, this version is shown to generate a random dynamical system (RDS) by a Wong–Zakai approximation, after which the existence of a random absorbing set is obtained via uniform apriori estimate of the solutions. Subsequently, the pullback asymptotic compactness of the RDS generated by the stochastic delayed HNNM is established and hence the existence of random attractors is obtained. Sufficient conditions under which the attractors turn out to be an exponential attracting stationary solution are also given. Finally, some numerical simulations illustrate the results.

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带延迟的随机 Hopfield 神经网络模型的随机吸引子

通过研究随机吸引子的存在和结构，探讨了具有延迟的随机霍普菲尔德神经网络模型（HNNM）的全局渐近行为。首先证明了随机延迟 HNNM 的轨迹场有一个几乎确定的连续版本，它对\(t>\tau \)是紧凑的（其中\(\tau \)是延迟），其构造基于穆罕默德（Stoch. Stoch.）然后，通过 Wong-Zakai 近似法证明了这一版本生成了随机动力系统（RDS），之后通过对解的均匀先验估计得到了随机吸收集的存在。随后，建立了随机延迟 HNNM 生成的 RDS 的回拉渐近紧凑性，从而得到了随机吸引子的存在。还给出了吸引子变成指数吸引静止解的充分条件。最后，一些数值模拟对结果进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.