一类捕食-食饵模型的共存性

Coexistence in a predator-prey model

研究了一类具有一般形式反应函数的捕食-食饵模型的正解.给出了正解的先验估计,利用不动点指标原理讨论了正解的存在性.通过计算degW′(I-F,D)、indexW′(F,(0,0))和indexW′(F,(θ,0)),得出食饵和捕食者可以共存当且仅当捕食者的死亡率c控制在下限-d2λ0和上限-λ1(d2,-efv(θ,0))之间,且食饵的固有增长率超过d1λ0.

The positive solutions are investigated for a predator-prey model with general functional response. A priori estimation to the positive solutions of the model is given, and the fixed point index theory is utilized for discussing the existence of the positive solutions. By calculating degw,（I-F,D）,indexw,（F,（0,0）） and indexw, （F, （0, 0）） , we obtain that predator and prey coexist if and only if predator＇s death rate c is controlled between the lower limit -d2λ0 and the upper limit -λ1 （d2,-efv（θ,0））, and prey＇s inherent growth rate is lager than d1λ0.