基于比率的三种群生态模型的建立及其稳定性  

The establishment of three-species ratio-dependent ecological model and its stability

作　　者：杨小康[1,2] 窦霁虹[1] 孙艳艳[1] 

机构地区：[1]西北大学数学系,西安710127 [2]西安文理学院数学系,西安710065

出　　处：《齐齐哈尔大学学报（自然科学版）》2009年第3期74-76,共3页Journal of Qiqihar University(Natural Science Edition)

摘　　要：建立了基于比率的地下植物、地上植物、食草动物3种群生态模型,采用微分方程稳定性分析方法,对系统的稳定性进行了分析,讨论了系统边际平衡点的稳定性,并证明了这个系统正平衡点的存在性及其全局稳定性。In this paper, a three-species ratio-dependent ecological model is established about the underground plant, the above-ground plant and the herbivore. The stability of boundary equilibrium point of the system is studied and the existence of the positive equilibrium point is proved. Some conditions are derived for the local asymptotic stability of the positive equilibrium.

关 键 词：捕食系统 稳定性 比率型 全局稳定性 

分 类 号：O175.14[理学—数学]