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

摘要： 研究了一类具有饱和竞争项及修正的Leslie-Gower（简记为L-G）功能反应项的捕食扩散系统在齐次Neumann边界条件下的持续性和全局渐近稳定性。利用上下解方法与极值原理建立了该捕食系统的解先验估计和系统持续性成立的充分条件。利用抛物方程的比较原理及迭代序列收敛法，证明了该捕食系统常数正平衡解的全局渐近稳定性的充分条件。

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