# Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

Xiaoyao Jia; Juanjuan Gao; Xiaoquan Ding

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 586-602
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topXiaoyao Jia, Juanjuan Gao, and Xiaoquan Ding. "Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise." Open Mathematics 14.1 (2016): 586-602. <http://eudml.org/doc/286754>.

@article{XiaoyaoJia2016,

abstract = {In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.},

author = {Xiaoyao Jia, Juanjuan Gao, Xiaoquan Ding},

journal = {Open Mathematics},

keywords = {Gray-Scott equation; Random attractor; Random dynamical system; Multiplicative noise; random attractor; random dynamical system; multiplicative noise},

language = {eng},

number = {1},

pages = {586-602},

title = {Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise},

url = {http://eudml.org/doc/286754},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Xiaoyao Jia

AU - Juanjuan Gao

AU - Xiaoquan Ding

TI - Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 586

EP - 602

AB - In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.

LA - eng

KW - Gray-Scott equation; Random attractor; Random dynamical system; Multiplicative noise; random attractor; random dynamical system; multiplicative noise

UR - http://eudml.org/doc/286754

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.