Dynamics of a Gilpin-Ayala predator-prey system with state feedback weighted harvest strategy

Xiaohuan Yu; Mingzhan Huang; Xiaohuan Yu; Mingzhan Huang

doi:10.3934/math.20231380

AIMS Mathematics

2023, Volume 8, Issue 11: 26968-26990. doi: 10.3934/math.20231380

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Research article

Dynamics of a Gilpin-Ayala predator-prey system with state feedback weighted harvest strategy

Xiaohuan Yu ,
Mingzhan Huang ^,

College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Received: 02 August 2023 Revised: 12 September 2023 Accepted: 18 September 2023 Published: 22 September 2023
MSC : 34C60, 92D25, 92D40

The current research presents a predator-prey model that incorporates both a Gilpin-Ayala growth function and a Holling type Ⅲ functional response. Two Lyapunov functions are established to confirm the global asymptotic stability of the positive equilibrium $ P^{*} $ and the predator extinction equilibrium $ P_{k} $. Considering ecological protection and commercial incentives, we also incorporated a weighted harvesting strategy and pulse control into the model. We investigated intricate dynamical problems instigated by the weighting harvesting and pulse effects, and affirmed the existence and local asymptotic stability of both predator-extinction periodic solution and positive order-1 periodic solution. In the end, a suite of numerical simulations were carried out using MATLAB, aiming to corroborate the theoretical findings and deliver conclusions rooted in a biological context.
- predator-prey system,
- stability,
- periodic solution,
- Gilpin-Ayala growth,
- Holling Ⅲ functional response
Citation: Xiaohuan Yu, Mingzhan Huang. Dynamics of a Gilpin-Ayala predator-prey system with state feedback weighted harvest strategy[J]. AIMS Mathematics, 2023, 8(11): 26968-26990. doi: 10.3934/math.20231380

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Abstract

The current research presents a predator-prey model that incorporates both a Gilpin-Ayala growth function and a Holling type Ⅲ functional response. Two Lyapunov functions are established to confirm the global asymptotic stability of the positive equilibrium $ P^{*} $ and the predator extinction equilibrium $ P_{k} $. Considering ecological protection and commercial incentives, we also incorporated a weighted harvesting strategy and pulse control into the model. We investigated intricate dynamical problems instigated by the weighting harvesting and pulse effects, and affirmed the existence and local asymptotic stability of both predator-extinction periodic solution and positive order-1 periodic solution. In the end, a suite of numerical simulations were carried out using MATLAB, aiming to corroborate the theoretical findings and deliver conclusions rooted in a biological context.

References

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