TY - JOUR T1 - Asymptotic Behavior for Generalized Ginzburg-Landau Population Equation with Stochastic Perturbation AU - Xu , Jiahe AU - Zhou , Kang AU - Lu , Qiuying JO - Annals of Applied Mathematics VL - 2 SP - 174 EP - 182 PY - 2022 DA - 2022/06 SN - 32 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20636.html KW - Ginzburg-Landau model, additive white noise, random attractor, Hausdorff dimension. AB -

In this paper, we are devoted to the asymptotic behavior for a nonlinear parabolic type equation of higher order with additive white noise. We focus on the Ginzburg-Landau population equation perturbed with additive noise. Firstly, we show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. And then, it is proved that under some growth conditions on the nonlinear term, this stochastic equation has a compact random attractor, which has a finite Hausdorff dimension.