一类修正的Leslie-Gower型扩散捕食系统的定性分析

摘要/Abstract

摘要：

该文讨论了带有Robin边界条件的一类修正Leslie-Gower型捕食系统, 建立了系统共存解的存在性、稳定性与不存在性, 并讨论了抛物系统的长时间行为. 结果表明, 系统中种群的内秉增长率及椭圆问题Robin边界条件下的主特征值在讨论系统正共存解的存在性与不存在性以及种群的灭绝中发挥了重要作用.

关键词: 捕食系统, 扩散, 共存解, 功能反应, 不动点指数

Abstract:

This paper is concerned with a modified Leslie-Gower predator-prey system with Robin boundary conditions. The existence/nonexistence and stability of coexistence solutions are obtained. Furthermore, the long-time behavior of parabolic system is also investigated. The results show that the intrinsic growth rates and the principle eigenvalues of the corresponding elliptic problems with respect to the Robin boundary conditions play more important roles than other parameters for the existence/nonexistence of nonconstant positive steady-state
solutions and the extinction of the species.

Key words: Predator-prey system, Diffusion, Coexistence solutions, Functional response, Fixed point index

中图分类号:

35J60

史红波, 李万同, 林国. 一类修正的Leslie-Gower型扩散捕食系统的定性分析[J]. 数学物理学报, 2011, 31(5): 1403-1415.

SHI Hong-Bo, LI Wan-Tong, LIN Guo. Qualitative Analysis of a Modified Leslie-Gower Predator-Prey System with Diffusion[J]. Acta mathematica scientia,Series A, 2011, 31(5): 1403-1415.

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