一类比率依赖捕食与被捕食系统的定性分析  

Qualitative Analysis of a Ratio-Dependent Predator-Prey System

作　　者：梁志清[1] 

机构地区：[1]玉林师范学院数学与计算机科学系,广西玉林537000

出　　处：《广西科学院学报》2008年第3期177-180,共4页Journal of Guangxi Academy of Sciences

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.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.

关 键 词：比率依赖 全局渐近稳定 极限环 

分 类 号：O175.12[理学—数学]