Markovian switching induced dynamics of a predator-prey system with prey refuge and habitat selection

Yuan Tian; Jing Zhu; Haiyan Gao; Kaibiao Sun; Yuan Tian; Jing Zhu; Haiyan Gao; Kaibiao Sun

doi:10.3934/era.2026045

Electronic Research Archive

2026, Volume 34, Issue 2: 962-996. doi: 10.3934/era.2026045

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Research article

Markovian switching induced dynamics of a predator-prey system with prey refuge and habitat selection

Yuan Tian ^{1
,
,},
Jing Zhu ¹,
Haiyan Gao ^{2
,
,},
Kaibiao Sun ^{3
,
,}

1.
School of Science, Dalian Maritime University, Dalian 116026, China
2.
Department of Public Education, Dalian University of Finance and Economics, Dalian 116622, China
3.
School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China

Received: 17 December 2025 Revised: 19 January 2026 Accepted: 23 January 2026 Published: 29 January 2026

In natural ecosystems, population dynamics are influenced by white and colored noise, which drive the population system to transition between multiple states. Therefore, it is essential to investigate predator-prey models that incorporate the concurrent impacts of white and colored noise. In this paper, we examined a three-dimensional stochastic predator-prey model involving dual prey species and a single predator by incorporating the refuge effect and habitat selection behavior under Markovian switching. By leveraging the theoretical framework of stochastic differential equations, its stochastic persistence was analyzed. Additionally, by constructing suitable Lyapunov functions, the conditions for an ergodic stationary distribution were deduced. Additionally, the extinction of populations and the asymptotic properties of solutions were explored. The findings revealed that habitat selection behavior has a significant and detrimental impact on the corresponding prey, while the refuge effect positively influences the prey and the predator. Ultimately, numerical simulations were performed to validate the theoretical outcomes. The results of these simulations strongly confirm the accuracy of the theoretical deductions.
- glipin-ayala model,
- Markov switching,
- stationary distribution,
- persistence
Citation: Yuan Tian, Jing Zhu, Haiyan Gao, Kaibiao Sun. Markovian switching induced dynamics of a predator-prey system with prey refuge and habitat selection[J]. Electronic Research Archive, 2026, 34(2): 962-996. doi: 10.3934/era.2026045

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Abstract

In natural ecosystems, population dynamics are influenced by white and colored noise, which drive the population system to transition between multiple states. Therefore, it is essential to investigate predator-prey models that incorporate the concurrent impacts of white and colored noise. In this paper, we examined a three-dimensional stochastic predator-prey model involving dual prey species and a single predator by incorporating the refuge effect and habitat selection behavior under Markovian switching. By leveraging the theoretical framework of stochastic differential equations, its stochastic persistence was analyzed. Additionally, by constructing suitable Lyapunov functions, the conditions for an ergodic stationary distribution were deduced. Additionally, the extinction of populations and the asymptotic properties of solutions were explored. The findings revealed that habitat selection behavior has a significant and detrimental impact on the corresponding prey, while the refuge effect positively influences the prey and the predator. Ultimately, numerical simulations were performed to validate the theoretical outcomes. The results of these simulations strongly confirm the accuracy of the theoretical deductions.

References

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