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 - <p style="text-align: justify;">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.</p>