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Research Article | Open Access

Long-time dynamics of a stochastic multimolecule oscillatory reaction model with Poisson jumps

Yongchang Wei1( ), Zongbin Yin2
School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China
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Abstract

This paper reveals dynamical behaviors in the stochastic multimolecule oscillatory reaction model with Poisson jumps. First, this system is proved to have a unique global positive solution via the Lyapunov technique. Second, the existence and uniqueness of general random attractors for its stochastic homeomorphism flow is proved by the comparison theorem, and meanwhile, a criterion for the existence of singleton sets is obtained. Finally, numerical simulations are used to illustrate the predicted random attractors.

Keywords

multimolecule oscillatory reaction modelrandom attractorsuniquenesssingleton sets
CLC number: 34E10, 60H10, 60J75

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2956-2972
DOI: 10.3934/math.2022163

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Cite this article:
Wei Y, Yin Z. Long-time dynamics of a stochastic multimolecule oscillatory reaction model with Poisson jumps. AIMS Mathematics, 2022, 7(2): 2956-2972. https://doi.org/10.3934/math.2022163

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Received: 05 July 2021
Accepted: 18 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)