Limit cycles in a general Kolmogorov model

被引：35

作者：

Huang, XC ^{[1
]}

Zhu, LM ^{[1
]}

机构：

[1] Yangzhou Polytech Univ, Dept Math, Yangzhou 225002, Jiangsu, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 60卷 / 08期

关键词：

limit cycle; predator-prey system; Kolmogorov model;

D O I：

10.1016/j.na.2004.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of limit cycles is interesting and significant both in theory and applications. In mathematical ecology, finding models that display a stable limit cycle-an attracting stable self-sustained oscillation, is a primary work. In this paper, a general Kolmogorov system, which includes the Gause-type model (Math. Biosci. 88 (1988) 67) the general predator-prey model (J. Phys. A: Math. Gen. 21 (1988) L685; Math. Biosci. 96 (1989) 47), and many other models (J. Biomath. 15(3) (2001) 266; J. Biomath. 16(2) (2001) 156; J. Math. 21(22) (2001) 145), is studied. The conditions for the existence and uniqueness of limit cycles in this model are proved. Some known results are easily derived as an illustration of our work. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：1393 / 1414

页数：22

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