稀疏效应下第Ⅲ类功能性反应系统的极限环存在性和唯一性

Existence and uniqueness of limit cycles for type Ⅲ functional response system with sparse effect

研究了数学生态学中一类稀疏效应下第Ⅲ类功能性反应系统,应用微分方程定性理论和Poinca-re-Bendison环域理论,获得了该系统存在极限环和存在唯一极限环的条件。证明了在满足该条件的情况下,捕食者、食饵两种群永远不会灭绝。

Functional response system of Type Ⅲ with sparse effect is investigated, and the sufficient conditions of existence and uniqueness of limit cycles was studied using differential equation qualitative theory and the Poincare-Bendison rings theory. It has been certificated that the predator group and the prey group will never be extinguished under sufficient condition.