一类修正的Leslie-Gower型扩散捕食系统的定性分析

Abstract

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

CLC Number:

35J60

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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Qualitative Analysis of a Modified Leslie-Gower Predator-Prey System with Diffusion

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