一类蜘蛛-昆虫模型平衡态正解的存在性

The existence of steady-state positive solutions for a spider-insect model

研究一类单食饵-双捕食者的蜘蛛-昆虫模型。利用特征值变分原理和极值原理给出正解的先验估计及正解存在的必要条件。应用空间分解和隐函数定理得到正解存在的充分条件。结果表明,在特定条件下,系统共存态依赖于昆虫的生长率。

A one-prey-two-predator spider-insect model is studied. By the variational principle of eigenvalue and the Maximum principle,priori estimates and the necessary conditions of existence for positive solutions are given. Applying the method of space decomposition and implicit function theorem,a sufficient condition of existence of positive solutions is obtained. The results show that,under certain conditions,the coexistence depends on the growth rate of insects.