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<p>In this paper, we study the pathwise dynamics of stochastic delay <i>p</i>-Laplacian lattice systems under Wong-Zakai type approximations. First, we rigorously establish the existence and uniqueness of pullback random attractors for the approximate system, which features a broad class of nonlinear diffusion terms. Subsequently, for a delayed system driven by affine noise, we demonstrate the convergence of solutions and the upper semicontinuity of random attractors as the Wiener shift step-length approaches <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>0</mn> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>. Finally, we characterize the limiting behavior of random attractors in autonomous systems when simultaneously taking the Wiener shift step-length and time delay parameter to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(0^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>0</mn> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>.</p>

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Wong-Zakai Approximations and Pathwise Dynamical Behavior for Stochastic Delay p-Laplacian Lattice Systems

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Ke Xiao,
  • Jun Shen

摘要

In this paper, we study the pathwise dynamics of stochastic delay p-Laplacian lattice systems under Wong-Zakai type approximations. First, we rigorously establish the existence and uniqueness of pullback random attractors for the approximate system, which features a broad class of nonlinear diffusion terms. Subsequently, for a delayed system driven by affine noise, we demonstrate the convergence of solutions and the upper semicontinuity of random attractors as the Wiener shift step-length approaches \(0^{+}\) 0 + . Finally, we characterize the limiting behavior of random attractors in autonomous systems when simultaneously taking the Wiener shift step-length and time delay parameter to \(0^{+}\) 0 + .