Uniform attractors of stochastic two-compartment Gray-Scott system with multiplicative noise

Junwei Feng; Hui Liu; Jie Xin

doi:10.3934/dcdsb.2020116

Article Contents

2020, Volume 25, Issue 12: 4617-4640. Doi: 10.3934/dcdsb.2020116

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Uniform attractors of stochastic two-compartment Gray-Scott system with multiplicative noise

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
2.
College of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China

^* Corresponding author: Jie Xin
^* Corresponding author: Jie Xin

Received: August 31, 2019

Revised: December 31, 2019

Early access: March 2020

Published: December 2020

The second author is supported by the Natural Science Foundation of Shandong under Grant No. ZR2018QA002, the National Natural Science Foundation of China No. 11901342 and China Postdoctoral Science Foundation No. 2019M652350. The third author is supported by the NSF of China (No. 11371183) and the NSF of Shandong Province (No. ZR2013AM004)

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Abstract

We first show that the stochastic two-compartment Gray-Scott system generates a non-autonomous random dynamical system. Then we establish some uniform estimates of solutions for stochastic two-compartment Gray-Scott system with multiplicative noise. Finally, the existence of uniform and cocycle attractors is proved.

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Mathematics Subject Classification: 35K51, 37C70, 35B41.

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