一类具功能性反应的食饵-捕食者两种群模型的稳定性

Qualitative of a Class Two Species Predator-Prey Model with Functional Response

研究具功能性反应的食饵-捕食者两种群模型:dx/dt=x(a-r1x)-bxyα/(1+ωx),dy/dt=-r2y+cxy/(1+ωx),α≥1时系统平衡点的性态和全局稳定性,利用B end ixson环域定理证明极限环的存在性,根据张芷芬惟一性定理证明极限环的惟一性.

This paper introduces a kind food with functional response-two groups types of predators dx/dt = x（a - r1x） - bxy^α/（1 ＋ ωx） ,dy/dt = -r2y ＋ cxy/（1＋ωx） ,α ≥ 1. The quality of the balance point and the global stability are discussed in this system. The existence of the limit circle is proved by Bendixson Theoroem. The uniqueness of the limit circle around the neighborhood of positive equilibrium is exploited by Uniqueness Theoroem of Zheng Zifen.