一类修正的Leslie-Gower型扩散捕食系统的定性分析  

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

作　　者：史红波[1,2] 李万同[2] 林国[2] 

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223300 [2]兰州大学数学与统计学院,兰州730000

出　　处：《数学物理学报（A辑）》2011年第5期1403-1415,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(10871085;10801065);甘肃省自然科学基金(096RJZA051)资助

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.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. Fhrthermore, 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.

关 键 词：捕食系统 扩散 共存解 功能反应 不动点指数 

分 类 号：O175.12[理学—数学]