食饵种群具有群体防御能力的Ⅰ类功能性反应的捕食系统

Ⅰ Functional Response Prey-predator System While the Prey Population Has Group Defense Ability

对一类食饵种群具有群体防御能力且其功能性反应函数为 类的捕食者—食饵种群系统进行了定性分析 ,得到了系统奇点的一些性态及其全局稳定性 ,并且利用 L iapunov函数法和Poincare- Bendixson定理得到了系统至少存在两个极限环的充分条件 .最后对模型做了进一步推广 .

Qualitative analysis of functional response prey- predator system while the prey population has group defense ability is studied in this paper.Some properties of the singular points of the system and its global stability are discussed;By utilizing the method of Lia- punov function and the Poincare- Bendixson theorem,the sufficientcondition of the existence of at least two limit cycles of the system is obtained.