In this paper, we consider dynamical behaviour for stochastic discrete complex Ginzburg–Landau equations driven by locally Lipschitz nonlinear noise. We prove the existence and uniqueness of solutions. Thus the solution operators generate mean random dynamical systems. Finally, the existence and uniqueness for weak pullback random attractors in ${\ell }^2$ are established.

中文翻译：

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非线性噪声驱动的非自治离散复Ginzburg-Landau方程的渐近行为

在本文中，我们考虑了由局部 Lipschitz 非线性噪声驱动的随机离散复数 Ginzburg-Landau 方程的动力学行为。我们证明解的存在性和唯一性。因此，求解算子生成平均随机动力系统。最后，弱回拉随机吸引子的存在唯一性${\ell }^2$ 成立。