Boundedness and stability analysis of the two species predator-prey model with prey-taxis and nonlinear growth rate in predator

Jianhua Li; YingYuan Mi; Jianhua Li; YingYuan Mi

doi:10.3934/era.2025331

Electronic Research Archive

2025, Volume 33, Issue 12: 7509-7527. doi: 10.3934/era.2025331

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Boundedness and stability analysis of the two species predator-prey model with prey-taxis and nonlinear growth rate in predator

Jianhua Li ¹,
YingYuan Mi ^{2
,
,}

1.
School of Mathematics, Hexi University, Gansu 734000, China
2.
School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China

Received: 13 October 2025 Revised: 29 November 2025 Accepted: 05 December 2025 Published: 15 December 2025

In this paper, we study initial-boundary value problem of a predator-prey model with taxis strategies and a nonlinear growth rate for the predator. We establish that, for any spatial dimension $ (N \geq 1) $, the model admits positive classical solutions that are globally existent and uniformly bounded. Our results demonstrate that the nonlinear growth rate can effectively restrain the aggregation of predators. Furthermore, by constructing a suitable energy functional and combining it with the previously established uniform boundedness result, we analyze the global asymptotic stability of the coexistence steady state.
- predator-prey model,
- nonlinear grow rate,
- existence,
- boundedness,
- dynamics behavior,
- global stability
Citation: Jianhua Li, YingYuan Mi. Boundedness and stability analysis of the two species predator-prey model with prey-taxis and nonlinear growth rate in predator[J]. Electronic Research Archive, 2025, 33(12): 7509-7527. doi: 10.3934/era.2025331

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Abstract

In this paper, we study initial-boundary value problem of a predator-prey model with taxis strategies and a nonlinear growth rate for the predator. We establish that, for any spatial dimension $ (N \geq 1) $, the model admits positive classical solutions that are globally existent and uniformly bounded. Our results demonstrate that the nonlinear growth rate can effectively restrain the aggregation of predators. Furthermore, by constructing a suitable energy functional and combining it with the previously established uniform boundedness result, we analyze the global asymptotic stability of the coexistence steady state.

References

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