Qualitative analysis on the diffusive Holling–Tanner predator–prey model

We consider the diffusive Holling–Tanner predator–prey model subject to the homogeneous Neumann boundary condition. We first apply Lyapunov function method to prove some global stability results of the unique positive constant steady-state. And then, we derive a non-existence result of positive non-...

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Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2023; no. 41; pp. 1 - 10
Main Authors Zhao, Xu, Zhou, Wenshu
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2023
Subjects
global stability
holling–tanner predator–prey model
lyapunov function method
sel'kov model
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Summary:We consider the diffusive Holling–Tanner predator–prey model subject to the homogeneous Neumann boundary condition. We first apply Lyapunov function method to prove some global stability results of the unique positive constant steady-state. And then, we derive a non-existence result of positive non-constant steady-states by a novel approach that can also be applied to the classical Sel'kov model to obtain the non-existence of positive non-constant steady-states if 0 < p ≤ 1 .
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2023.1.41