| 摘要: |
| 研究一类比率依赖的捕食与被捕食系统.首先给出系统的有界性及持久性;其次给出边界平衡点及正平衡点的全局渐近稳定性;最后证明当正平衡点为不稳定的焦(结)点时,系统存在唯一极限环. |
| 关键词: 比率依赖 全局渐近稳定 极限环 |
| DOI： |
| 投稿时间：2007-10-29修订日期：2008-05-04 |
| 基金项目: |
|
| Qualitative Analysis of a Ratio-Dependent Predator-Prey System |
|
LIANG Zhi-qing
|
| (Department of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi, 537000, China) |
| Abstract: |
| In this paper,a ratio-dependent predator-prey systems was studied.First,results on the boundedness of solutions, the permanence of the system,are presented.Second,the sufficient conditions for both global stabilities of positive equilibrium and boundary equilibrium are established.Finally,it is proved that when the positive equilibrium becomes unstable,system has a unique limit cycle. |
| Key words: ratio-dependent global asymptotic stability limit cycles |
