Gause型食物链模型Hopf分支的存在性分析  

The Existence of Hopf Bifurcation Analysis on General Gause-type Predator-prey Model

作　　者：郭爽[1] 姜秀燕[1] 于健[1] 乔兴[1] 

机构地区：[1]大庆师范学院数学科学学院,黑龙江大庆163712

出　　处：《数学的实践与认识》2012年第22期167-175,共9页Mathematics in Practice and Theory

基　　金：黑龙江省普通高等学校青年学术骨干支持项目(11251G0011)

摘　　要：考虑了一类三维时滞Gause型食物链模型.首先分析了共存平衡点稳定的条件,然后利用多项式理论分析了特征方程特征根的分布,得到了Hopf分支存在的条件,最后给出了几组数值模拟验证文中得到的结论,进一步预测了Hopf分支的全局存在性.A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of stability conditions are obtained for the coexisting equilibrium. Secondly, the existence of Hopf bifurcation are obtained via employing the polynomial theorem to analyze the distribution of the roots of the associated characteristic equation. Finally, some numerical simulations are carried out to illustrate the obtained results and we predict the global existance of Hopf bifurcation furthermore.

关 键 词：Gause型食物链 时滞 HOPF分支 

分 类 号：O175[理学—数学]