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

作　　者：Mengxin Chen Qianqian Zheng Mengxin Chen;Qianqian Zheng(College of Mathematics and Information Science, Henan Normal University, Xinxiang, China;School of Science, Xuchang University, Xuchang, China)

机构地区：[1]College of Mathematics and Information Science, Henan Normal University, Xinxiang, China [2]School of Science, Xuchang University, Xuchang, China

出　　处：《Applied Mathematics》2022年第8期658-671,共14页应用数学（英文）

摘　　要：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.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.

关 键 词：Predator-Prey Model Global Asymptotic Stability Prey-Taxis Lyapunov Function 

分 类 号：O175[理学—数学]