Global Stability of a Three-Species System with Attractive Prey-Taxis

Mengxin Chen¹, Qianqian Zheng^2
1College of Mathematics and Information Science, Henan Normal University, Xinxiang, China.
²School of Science, Xuchang University, Xuchang, China.

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.

Keywords

Predator-Prey Model, Global Asymptotic Stability, Prey-Taxis, Lyapunov Function