Boundedness and asymptotic behavior of a prey-taxis model with modified Leslie-Gower and hunting cooperation

Weibo Lin; Lu Xu; Weibo Lin; Lu Xu

doi:10.3934/math.2026176

AIMS Mathematics

2026, Volume 11, Issue 2: 4395-4414. doi: 10.3934/math.2026176

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Research article

Boundedness and asymptotic behavior of a prey-taxis model with modified Leslie-Gower and hunting cooperation

Weibo Lin ¹,
Lu Xu ^{1,2
,
,}

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

Received: 22 December 2025 Revised: 19 January 2026 Accepted: 27 January 2026 Published: 12 February 2026
MSC : 35A01, 35B35, 35K57, 92C17

This work investigated the dynamics of a prey-taxis model with modified Leslie-Gower and hunting cooperation. Using energy estimates combined with a newly developed weighted technique, we proved that solutions remain globally bounded in both two or higher dimensions, provided the prey-taxis coefficient is sufficiently small. Furthermore, by constructing a suitable Lyapunov functional, we analyzed the large-time behavior of solutions under some conditions.
- Leslie-Gower,
- hunting cooperation,
- boundedness,
- large time behavior
Citation: Weibo Lin, Lu Xu. Boundedness and asymptotic behavior of a prey-taxis model with modified Leslie-Gower and hunting cooperation[J]. AIMS Mathematics, 2026, 11(2): 4395-4414. doi: 10.3934/math.2026176

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Abstract

This work investigated the dynamics of a prey-taxis model with modified Leslie-Gower and hunting cooperation. Using energy estimates combined with a newly developed weighted technique, we proved that solutions remain globally bounded in both two or higher dimensions, provided the prey-taxis coefficient is sufficiently small. Furthermore, by constructing a suitable Lyapunov functional, we analyzed the large-time behavior of solutions under some conditions.

References

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