Methods and Applications of Analysis

Volume 23 (2016)

Number 3

Global stability of Leslie-type predator-prey model

Pages: 259 – 268

DOI: http://dx.doi.org/10.4310/MAA.2016.v23.n3.a3

Authors

Yuanwei Qi (Department of Mathematics, University of Central Florida, Orlando, Fl., U.S.A.)

Yi Zhu (Department of Mathematics, University of Central Florida, Orlando, Fl., U.S.A.)

Abstract

In this paper we study the global stability of diffusive predator-prey system of Leslie type in a bounded domain $\Omega \subset R^N$ with no-flux boundary condition. By using a new approach, we establish much improved global asymptotic stability of the unique positive equilibrium solution. We also show how to extend the result to more general type of systems with non-homogeneous environment and/or wider class of kinetic terms.

Keywords

global asymptotic stability, predator-prey, positive equilibrium solution, comparison principle, reaction-diffusion

2010 Mathematics Subject Classification

34C20, 34C25, 92E20

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