带有加法Allee效应的捕食-食饵模型共存解的惟一性和多解性

带有加法Allee效应的捕食-食饵模型共存解的惟一性和多解性 Uniqueness and Multiplicity of Coexistence Solutions for a Predator-Prey Model with Additive Allee Effect 李海侠 LI Haixia 1 first-author 宝鸡文理学院数学与信息科学学院 宝鸡文理学院数学与信息科学学院 Institute of Mathematics and Information Science,Baoji University of Arts and Sciences Institute of Mathematics and Information Science,Baoji University of Arts and Sciences 利用不动点指数理论给出了一类带有加法Allee效应的捕食-食饵模型正解存在的充分条件,讨论了正解的惟一性和稳定性,运用扰动理论研究了参数b2充分大时正解的多重性.结果表明在一定条件下系统存在多重解和惟一解. The sufficient conditions of the existence of positive solutions for a predator-prey model with additive Allee effect are given by means of the fixed point index.Then,the uniqueness and stability of positive solutions are investigated.Finally,the multiplicity of positive solutions is determined by resorting to perturbation theory when b2 is sufficiently large.The results show that the system has multiple solutions and unique solution under appropriate conditions. Allee效应 不动点指数 惟一性 多解性 Allee affect fixed point index uniqueness multiplicity 10.14188/j.1671-8836.2015.04.004 O175 中央高校基本科研业务费专项资金资助（GK201302025）;陕西省教育厅专项科研计划资助项目（14JK1035）;宝鸡文理学院重点科研项目（ZK15039） 2015-04-01 2021-03-31 4 61