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<p>In this paper, we prove that the model of stochastic lattice dynamical system driven by a fractional Brownian motion with Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H\in (1/2,1)\)</EquationSource> </InlineEquation> proposed in [<CitationRef CitationID="CR3">3</CitationRef>, Bessaih&#xa0;et&#xa0;al.&#xa0;2017] under the same proper conditions possesses a random attractor, which turns out to have component singleton sets. The result improves the one in [<CitationRef CitationID="CR14">14</CitationRef>, Gu&#xa0;2013].</p>

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Singleton Sets Random Attractors for Lattice Dynamical Systems Driven by a Fractional Brownian Motion Revisited

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Anhui Gu

摘要

In this paper, we prove that the model of stochastic lattice dynamical system driven by a fractional Brownian motion with Hurst parameter \(H\in (1/2,1)\) proposed in [3, Bessaih et al. 2017] under the same proper conditions possesses a random attractor, which turns out to have component singleton sets. The result improves the one in [14, Gu 2013].