| Ivlev型捕食系统的全局动力学分析 |
| |
| 引用本文： | 肖海滨.Ivlev型捕食系统的全局动力学分析[J].应用数学和力学,2007,28(4):419-427. |
| |
| 作者姓名： | 肖海滨 |
| |
| 作者单位： | 宁波大学,数学系,浙江,宁波,315211;南京大学,数学系,南京,210093 |
| |
| 基金项目： | 浙江省宁波市自然科学基金 |
| |
| 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.
|
| 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 |
| 文章编号： | 1000-0887（2007）04-0419-09 |
| 修稿时间： | 2006-05-12 |
Global Analysis of Ivlev's Type Predator-Prey Dynamical System |
| |
| XIAO Hai-bin.Global Analysis of Ivlev''''s Type Predator-Prey Dynamical System[J].Applied Mathematics and Mechanics,2007,28(4):419-427. |
| |
| Authors: | XIAO Hai-bin |
| |
| Institution: | 1. Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211 ,P. R. China; 2. Department of Mathematics, Nanjing University, Nanjing 210093,P. R. China |
| |
| Abstract: | 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. |
| |
| Keywords: | limit cycle global stability density restrict Ivlev type functional response existence and uniqueness |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
