Analysis of a Holling-type IV stochastic prey-predator system with anti-predatory behavior and Lévy noise

Chuanfu Chai; Yuanfu Shao; Yaping Wang; Chuanfu Chai; Yuanfu Shao; Yaping Wang

doi:10.3934/math.20231071

AIMS Mathematics

2023, Volume 8, Issue 9: 21033-21054. doi: 10.3934/math.20231071

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Research article

Analysis of a Holling-type IV stochastic prey-predator system with anti-predatory behavior and Lévy noise

College of Science, Guilin University of Technology, Guilin, Guangxi 541004, China

Received: 08 May 2023 Revised: 13 June 2023 Accepted: 24 June 2023 Published: 03 July 2023
MSC : 92D15, 92B20

In this paper, we investigate a stochastic prey-predator model with Holling-type IV functional responses, anti-predatory behavior (referring to prey resistance to predator), gestation time delay of prey and Lévy noise. We investigate the existence and uniqueness of global positive solutions through Itô's formulation and Lyapunov's method. We also provide sufficient conditions for the persistence and extinction of prey-predator populations. Additionally, we examine the stability of the system distribution and validate our analytical findings through detailed numerical simulations. Our paper concludes with the implications of our results.
- Holling-type IV,
- anti-predation,
- Lévy noise,
- persistence and extinction,
- stability in distribution
Citation: Chuanfu Chai, Yuanfu Shao, Yaping Wang. Analysis of a Holling-type IV stochastic prey-predator system with anti-predatory behavior and Lévy noise[J]. AIMS Mathematics, 2023, 8(9): 21033-21054. doi: 10.3934/math.20231071

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Abstract

In this paper, we investigate a stochastic prey-predator model with Holling-type IV functional responses, anti-predatory behavior (referring to prey resistance to predator), gestation time delay of prey and Lévy noise. We investigate the existence and uniqueness of global positive solutions through Itô's formulation and Lyapunov's method. We also provide sufficient conditions for the persistence and extinction of prey-predator populations. Additionally, we examine the stability of the system distribution and validate our analytical findings through detailed numerical simulations. Our paper concludes with the implications of our results.

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