BIFURCATIONS OF DEGENERATE SINGULAR POINT OF A PREDATOR-PREY SYSTEM WITH HOLLING-IV FUNCTIONAL RESPONSE

• 作者: Jiangbin Chen
• 来源期刊: 微分方程年刊：英文版
• 学科: 生物学
• 关键词: 捕食与被捕食系统 功能反应 鞍结分岔 奇点 退化 分叉现象 霍普夫分岔 计算机模拟
• 年，卷（期）: 2014,（4）
• 页码范围: 386-393
• 页数: 8页
• 分类号: Q141

摘要

A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium?which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Different kinds of bifurcation phenomena are exhibited, which include the saddle~node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions.