| 摘要: |
讨论一类食饵种群被开发的两种群捕食系统
{(dy/dt)=y(x-1),(dx/dt)=x(a0+a1-a2x2-a3y3)+s0,
(其中a0>0,a2>0,a3>0,s0>0,a1不定号)、平衡点的行为以及系统的全局稳定性.用Bendixson环域定理证明极限环的存在性,由张芷芬唯一性定理证明极限环的唯一性,同时对相应结论的生态学意义给予说明. |
| 关键词: 捕食系统 极限环 平衡点 |
| DOI： |
| 投稿时间：2002-08-19 |
| 基金项目:广西师范大学数学青年科学基金资助。 |
|
| Qualitative Analysis of a Kind of Predator-Prey System Exploited |
|
Wei Yuming
|
| (Coll. of Math, and Comp. Sci., Guangxi Normal Univ., 3 Yucailu, Guilin, Guangxi, 541004, China) |
| Abstract: |
The system
{(dy/dt)=y(x-1),(dx/dt)=x(a0+a1-a2x2-a3y3)+s0,
(where a0>0,a2>0,a3>0,s0>0,a1 can be positive or negative),the behaviors of the equilibria and the global stability of the system are studied. The existence of the limit circle is proved by Bendixson Theroem. The uniqueness of the limit circle around the neighborhood of the positive equilibrium exploited by Uniqueness Theorem of Zhang Zifen. The significance of the conclusions are interpreted. |
| Key words: predator-prey system limit circle equilibrium |
