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| ASYMPTOTIC BEHAVIOR FOR GENERALIZED GINZBURG-LANDAU POPULATION EQUATION WITH STOCHASTIC PERTURBATION |
| Jiahe Xu,Kang Zhou,Qiuying Lu |
| (Dept. of Math., Zhejiang Sci-Tech University, Zhejiang 310018, PR China) |
| DOI： |
| Abstract: |
| 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. |
| Key words: Ginzburg-Landau model; additive white noise; random attractor; Hausdorff dimension |