一类具有非线性密度制约的捕食系统极限环的Hopf分支  

HOPF BIFURCATION IN A CLASS OF PREDATOR-PREY MODELS WITH NONLINEAR DENSITY DEPENDENT

作　　者：赵书红[1] 窦霁虹[1] 原冠秀[1] 

机构地区：[1]西北大学数学系,西安710069

出　　处：《南京大学学报（数学半年刊）》2008年第2期230-238,共9页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：陕西省自然科学基金资助项目(2003A07)

摘　　要：本文用定性分析的方法讨论了一类具有非线性密度制约的HollingⅡ型功能反应的食饵-捕食者模型,分析了模型的正平衡点性态,得出了模型的极限环不存在与存在的充分条件,以及在给定参数满足一定条件下,利用Hopf分支理论,得到至少出现两个或三个极限环的充分条件.The qualitative analysis to discuss a class of Predator-Prey Models of hollingⅡfunctional response with nonlinear density dependent is used in this paper,the behavior of the model with the pos- itive equilibriums is analysed and sufficient conditions of the existence and nonexistence of a limit cycle are obtained in the system.Meanwhile,on the basis of the Hopf-bifurcations,the sufficient conditions that there occur at least two or three limit cycles are found when the given parameters satisfy certain conditions.

关 键 词：非线性密度制约 食饵-捕食者模型 全局稳定性 极限环 HOPF分支 

分 类 号：O175.12[理学—数学]