一类具有Allee效应的捕食-食饵模型正解的唯一性和渐近行为

Asymptotic Behaviour and Uniqueness of Positive Solutions for a Predator-prey Model with Allee Effect

研究一类具有加法Allee效应的捕食-食饵扩散模型。首先利用特征值的比较原理和不动点指数理论给出正解存在的充要条件,接着运用扰动理论讨论参数c充分大时正解的唯一性和稳定性。研究表明在一定条件下系统存在唯一的稳定解。最后通过抛物系统的比较原理得到全局吸引子的存在条件。

A diffusive predator-prey model with additive Allee effect is studied. Firstly, the sufficient and neces-sary conditions of the existence of positive solutions are given by means of the comparison principle of eigenvalue and the fixed point index. By virtue of the perturbation theory, the uniqueness and stability of positive solutions are discussed when the parameters is sufficiently large. The results show that the system has stable and unique positive solution under certain conditions. Finally, the existence condition of the global attractor is obtained by the comparison principle of parabolic system.