Global dynamics of a predator-prey model with prey-taxis and hunting cooperation

Xuemin Fan; Wenjie Zhang; Lu Xu; Xuemin Fan; Wenjie Zhang; Lu Xu

doi:10.3934/era.2025076

Electronic Research Archive

2025, Volume 33, Issue 3: 1610-1632. doi: 10.3934/era.2025076

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Research article

Global dynamics of a predator-prey model with prey-taxis and hunting cooperation

1.
College of Mathematics and Statistics, Yili Normal University, Yining 835000, China
2.
Institute of Applied Mathematics, Yili Normal University, Yining 835000, China

Received: 10 December 2024 Revised: 22 February 2025 Accepted: 25 February 2025 Published: 20 March 2025

The mathematical analysis of spatiotemporal distributions in many species exhibiting different predation mechanisms has attracted considerable attention in biology and ecology. In this article, we investigated a prey-taxis model involving hunting cooperation, which has more strong coupling structures. Utilizing energy estimates and semigroup theory, the global boundness of its classical solution was established when the hunting cooperation is weak in two dimensions. By means of Lyapunov functionals, the global asymptotically stability of the non-negative constant steady-state solution for the discussed model was established under certain assumptions on parameters. These results enrich the related researches on the prey-taxis model with Lotka-Volterra functional response, which has been studied by Jin and Wang.
- prey-taxis,
- hunting cooperation,
- boundedness,
- long time behavior
Citation: Xuemin Fan, Wenjie Zhang, Lu Xu. Global dynamics of a predator-prey model with prey-taxis and hunting cooperation[J]. Electronic Research Archive, 2025, 33(3): 1610-1632. doi: 10.3934/era.2025076

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Abstract

The mathematical analysis of spatiotemporal distributions in many species exhibiting different predation mechanisms has attracted considerable attention in biology and ecology. In this article, we investigated a prey-taxis model involving hunting cooperation, which has more strong coupling structures. Utilizing energy estimates and semigroup theory, the global boundness of its classical solution was established when the hunting cooperation is weak in two dimensions. By means of Lyapunov functionals, the global asymptotically stability of the non-negative constant steady-state solution for the discussed model was established under certain assumptions on parameters. These results enrich the related researches on the prey-taxis model with Lotka-Volterra functional response, which has been studied by Jin and Wang.

References

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