Stability and bifurcation in two species predator-prey models

被引：9
|
作者：
Kusbeyzi, I. [1 ,3 ]
Aybar, O. O. [1 ,3 ]
Hacinliyan, A. [1 ,2 ,3 ,4 ]
机构：
[1] Yeditepe Univ, Dept Informat Syst & Technol, TR-34755 Istanbul, Turkey
[2] Yeditepe Univ, Dept Phys, TR-34755 Istanbul, Turkey
[3] Gebze Inst Technol, Dept Math, Kocaeli, Turkey
[4] Bogazici Univ, Dept Phys, Istanbul, Turkey
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 01期
关键词：
Hopf bifurcation; Lotka-Volterra model; Normal form; HOPF-BIFURCATION; LIMIT-CYCLES; SYSTEM; CHAOS;
D O I：
10.1016/j.nonrwa.2010.06.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Changes in the number and stability of equilibrium points in the Lotka-Volterra model as well as some of its generalizations that lead to qualitative changes in the behavior of the system as a function of some of its parameters are studied by bifurcation analysis. A generalization involving a cubic interaction as proposed by Nutku is shown to change the stability properties in a simple way and in particular cases introduce additional stability. Numerical methods and the approach provided by approximate techniques near equilibrium points are used in the analysis. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：377 / 387
页数：11
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