Author(s)

Mengxin Chen¹, Qianqian Zheng²

¹College of Mathematics and Information Science, Henan Normal University, Xinxiang, China.
²School of Science, Xuchang University, Xuchang, China.

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.

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

Chen, M. and Zheng, Q. (2022) Global Stability of a Three-Species System with Attractive Prey-Taxis. Applied Mathematics, 13, 658-671. doi: 10.4236/am.2022.138041.