关键词: 捕食系统, Leslie-Gower反应项, 持续性, 全局渐近稳定性

Abstract: This paper studies persistence property and global asymptotic stability of a predator-prey system with predator saturation competition and modified Leslie-Gower functional response under the Neumann boundary condition. By using the upper and lower solution method and the maximum principle, some prior estimates and sufficient condition on persistence property of the predator-prey system are established. By using the comparison principle and the sequence iteration method of parabolic equations, it obtains the sufficient condition of the global asymptotic stability of positive equilibrium solution of this system.

Key words: predator-prey system, Leslie-Gower response, persistence property, global asymptotic stability