Stationary distribution of a stochastic two-species Schoener's competitive system with regime switching

Hong Qiu; Yunzhe Liu; Yanzhang Huo; Rumei Hou; Wenhua Zheng; Hong Qiu; Yunzhe Liu; Yanzhang Huo; Rumei Hou; Wenhua Zheng

doi:10.3934/math.2023076

AIMS Mathematics

2023, Volume 8, Issue 1: 1509-1529. doi: 10.3934/math.2023076

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Research article

Stationary distribution of a stochastic two-species Schoener's competitive system with regime switching

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received: 10 August 2022 Revised: 28 September 2022 Accepted: 09 October 2022 Published: 21 October 2022
MSC : 60H10, 60H30, 92D25

This paper studies a stochastic two-species Schoener's competitive model with regime switching. We first investigate the sufficient conditions for the existence of a unique stationary distribution of the model. Then we prove that the convergence of transition probability to the stationary distribution is exponentially under some mild assumptions. Moreover, we also introduce several numerical simulations to validate the model against the biological significance.
- stationary distribution,
- Schoener's competitive model,
- random disturbances,
- ergodicity
Citation: Hong Qiu, Yunzhe Liu, Yanzhang Huo, Rumei Hou, Wenhua Zheng. Stationary distribution of a stochastic two-species Schoener's competitive system with regime switching[J]. AIMS Mathematics, 2023, 8(1): 1509-1529. doi: 10.3934/math.2023076

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Abstract

This paper studies a stochastic two-species Schoener's competitive model with regime switching. We first investigate the sufficient conditions for the existence of a unique stationary distribution of the model. Then we prove that the convergence of transition probability to the stationary distribution is exponentially under some mild assumptions. Moreover, we also introduce several numerical simulations to validate the model against the biological significance.

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