一种捕食-被捕食模型正平衡位置的稳定性

The Stability of the Positive Equilibrium of a Predator-Prey Model

本文在〔1〕、〔2〕、〔3〕的基础上，给出了一种捕食-被捕食模型并证明了：若时，该系统在中存在唯一的正平衡位置，且该平衡位置是局部渐近稳定的；若再加上条件K1≥1、K2≥1，则该平衡位置全局稳定．

This article deals with a class of predator-prey model which based on [1] [2] [3], and it is proved that when a2 <,a 2 <1,a1<1,the system has only one positive equilibrium in the region D = {(x, y):x >0,0 < y <--m ｝and the equilibrium is locally stable;if an additional condition K1,K2≥1 is added,the equilibrium is globally asymptotically stable inside D.