摘要
研究捕食者与食饵均具有线性密度制约的Ivlev型捕食动力系统.应用常微分方程定性方法,得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件.特别地,在一定条件下,证明了极限环的存在唯一性与正平衡点的局部不稳定性是等价的,正平衡点的局部稳定性隐含它的全局稳定性,因此,系统的全局动力学性质完全由正平衡点的局部性质所决定.
A class of Ivlev＇ s type predator-prey dynamic systems with prey and predator both having linear density restricts is considered. By using the qualitative methods of ODE, the positive equilibrium＇s global stability and existence and uniqueness of non-small amplitude stable limit cycle were obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the positive equilibrium＇ s local unstability and the positive equilibrium＇ s local stability implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
出处
《应用数学和力学》
CSCD
北大核心
2007年第4期419-427,共9页
Applied Mathematics and Mechanics
基金
宁波市自然科学基金资助项目(2006A610032)
关键词
极限环
全局稳定性
密度制约
Ivlev功能反应
存在唯一性
limit cycle
global stability
density restrict
Ivlev type functional response
existence and uniqueness
