摘要
研究了一类具功能性反应的食饵-捕食者两种群模型.利用微分方程定性理论,当给定参数满足一定条件下,讨论了该系统平衡点的稳定性态.运用Dulac函数法,得到了系统不存在闭轨的充分条件.运用Poincare-Bendixson环域定理,证明了极限环的存在性.运用张芷芬惟一性定理,证明了极限环的惟一性.
In this paper, a class of two species predator-prey model with functional response is studied. By using stability methods, when the given parameter meets certain conditions, the stability of equilibrium is discussed. The sufficient condition for nonexistence of the closed orbit is got by using the method of Dulac function. The existence and uniqueness of the limit cycle are proved by applying Poincare-Bendixson theorem and Zhang Zhifen＇ s Uniqueness theorem.
出处
《淮阴师范学院学报（自然科学版）》
CAS
2010年第1期14-18,共5页
Journal of Huaiyin Teachers College;Natural Science Edition
基金
福建省教育厅自然科学基金资助项目(JA05204)
福建省科技厅基金资助项目(2005K027)
关键词
平衡点
极限环
存在惟一性
equilibrium
limit cycle
existence and uniqueness
