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中文摘要：
本文研究一类具Holling-Ⅳ型功能反应函数的捕食者-食饵模型.对模型进行定性分析得知系统正解都是有界的;因此,当平衡点不稳定,系统至少存在一稳定的极限环.本文还运用Poincare形式级数法,得到了正平衡点至多为二阶稳定细焦点的结论.并基于Hopf分支理论得知系统在一定条件下至少存在两个极限环.
英文摘要：
A predator-prey system with Holling-Ⅳfunctional response is investigated. The qualitative analysis for the model indicates that the positive solutions of the system are all bounded,thus,when the equilibrium is unstable,the system has at least one stable limit cycle.By using the method of formal power series of Poincare,we get a result that the positive equilibrium is a stable fine-focus of order at most 2.Moreover, base on the theory of Hopf bifurcation,we obtain that the system at least has two limit cycles under certain conditions.
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