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

Yongchang Wei; Zongbin Yin; Yongchang Wei; Zongbin Yin

doi:10.3934/math.2022163

AIMS Mathematics

2022, Volume 7, Issue 2: 2956-2972. doi: 10.3934/math.2022163

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Research article

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

Yongchang Wei ^{1
,
,},
Zongbin Yin ²

1.
School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
2.
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China

Received: 05 July 2021 Accepted: 18 November 2021 Published: 23 November 2021
MSC : 34E10, 60H10, 60J75

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.
- multimolecule oscillatory reaction model,
- random attractors,
- uniqueness,
- singleton sets
Citation: Yongchang Wei, Zongbin Yin. Long-time dynamics of a stochastic multimolecule oscillatory reaction model with Poisson jumps[J]. AIMS Mathematics, 2022, 7(2): 2956-2972. doi: 10.3934/math.2022163

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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.

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