一类基于比率的捕食-食饵系统的全局稳定性分析  

Global Stability Analysis of a Ratio-Dependent Predator-Prey System

作　　者：鲁铁军[1] 王美娟[1] 刘妍[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《应用数学和力学》2008年第4期447-452,共6页Applied Mathematics and Mechanics

摘　　要：研究一类基于比率和具第Ⅲ类功能性反应的捕食-食饵系统.通过分析正平衡点的局部稳定性给出了系统正平衡点全局渐近稳定以及系统存在极限环的条件.运用Hopf分支理论讨论了当正平衡点是非双曲型时的情形.A ratio dependent predator-prey system with HoUing type Ⅲ functional response was considered. The sufficient condition of the global asymptotic stability for the positive equilibrium and the existence of the limit cycle were given by studying the locally asymptotic stability of the positive equilibrium. At last, the condition when the positive equilibrium is no hyperbolic equilibrium was discussed by Hopf bifurcation.

关 键 词：比率 全局渐近稳定 功能性反应 HOPF分支 

分 类 号：O175.13[理学—数学]