TITLE:
Global Stability of a Three-Species System with Attractive Prey-Taxis
AUTHORS:
Mengxin Chen, Qianqian Zheng
KEYWORDS:
Predator-Prey Model, Global Asymptotic Stability, Prey-Taxis, Lyapunov Function
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.8,
August
19,
2022
ABSTRACT: This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respectively. Our results illustrate that 1) the global asymptotic stability of the semi-trivial equilibrium does not involve the prey-taxis coefficients χ, ξ; 2) the global asymptotic stability of two boundary equilibria relies on a single prey-taxis coefficient χ and ξ, respectively; 3) the global asymptotic stability of the unique positive equilibrium depends on two prey-taxis coefficients χ and ξ.