关键词: 捕食系统, 平衡点, 极限环, 稳定性

Abstract:

With the help of PoincareBendixson theorem, the existence for the limit cycles about a kind of predatorprey systems with functional response x^·=xg(x)-yφ(x), y^·=y(-d+eφ(x)) was discussed, obtaining the sufficient conditions for nonexistence, existence and uniqueness of the limit cycles around an equilibrium point in the case of g(x)=a-bx^m, φ(x)=cx^θ, m=θ=k/n, n>2, 1≤k+.

Key words:  predatorprey system, equilibrium point, limit cycle, stability