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<p>In this paper, we apply the implicit Euler scheme to discretize the (random) Burgers-Huxley equation and establish the existence of a numerical attractor for the discrete Burgers-Huxley system. We demonstrate the upper semi-convergence of the numerical attractor to the global attractor as the step size tends to zero. Furthermore, we provide finite dimensional approximations for both the numerical and random attractors, proving the convergence of the truncated attractors as the state space dimension goes to infinity. Lastly, we establish the existence of a random attractor and show that the truncated random attractor upper semi-converges to the truncated global attractor as the noise intensity approaches zero.</p>

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Dynamics of Discrete Random Burgers-Huxley Systems: Attractor Convergence and Finite Dimensional Approximations

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Fang Su,
  • Xue Wang

摘要

In this paper, we apply the implicit Euler scheme to discretize the (random) Burgers-Huxley equation and establish the existence of a numerical attractor for the discrete Burgers-Huxley system. We demonstrate the upper semi-convergence of the numerical attractor to the global attractor as the step size tends to zero. Furthermore, we provide finite dimensional approximations for both the numerical and random attractors, proving the convergence of the truncated attractors as the state space dimension goes to infinity. Lastly, we establish the existence of a random attractor and show that the truncated random attractor upper semi-converges to the truncated global attractor as the noise intensity approaches zero.