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Global Stability of a Three-Species System with Attractive Prey-Taxis
College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
School of Science, Xuchang University, Xuchang, China
- 1 College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
- 2 School of Science, Xuchang University, Xuchang, China
Applied Mathematics·Volume 13 (2022)·Pages 658–671·Published 18 August 2022·DOI10.4236/am.2022.138041
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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 .
KeywordsPredator-Prey ModelGlobal Asymptotic StabilityPrey-TaxisLyapunov Function
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