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Volume 32, Issue 2
Asymptotic Behavior for Generalized Ginzburg-Landau Population Equation with Stochastic Perturbation

Jiahe Xu, Kang Zhou & Qiuying Lu

Ann. Appl. Math., 32 (2016), pp. 174-182.

Published online: 2022-06

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  • 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.

  • Keywords

Ginzburg-Landau model, additive white noise, random attractor, Hausdorff dimension.

  • AMS Subject Headings

35B40, 35B41, 37H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-32-174, author = {Xu , JiaheZhou , Kang and Lu , Qiuying}, title = {Asymptotic Behavior for Generalized Ginzburg-Landau Population Equation with Stochastic Perturbation}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {32}, number = {2}, pages = {174--182}, 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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20636.html} }
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.

Jiahe Xu, Kang Zhou & Qiuying Lu. (2022). Asymptotic Behavior for Generalized Ginzburg-Landau Population Equation with Stochastic Perturbation. Annals of Applied Mathematics. 32 (2). 174-182. doi:
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