摘要
该文研究了一类带有Leslie-Gower项和Crowley-Martin反应函数的食物链模型.运用不动点指数理论给出了正解存在的充分条件,进而利用椭圆型方程正则理论讨论了正解的不存在性、稳定性和唯一性.结果表明,当参数c充分大或有界时系统在不同条件下均存在唯一且线性稳定的正解.最后通过数值模拟对分析结果进行了验证和补充.
A food-chain model with Leslie-Gower and Crowley-Martin functional response is investigated in this paper. The sufficient conditions for the existence of positive solutions are given by means of the fixed point index. Furthermore, use the regularity theory of elliptic equations, the nonexistence, stability and uniqueness of positive solutions are discussed. The results show that there exists a unique linearly stable positive solution under different conditions when the parameter c is large or bounded. Finally, some numerical simulations are presented to verify and complement the theoretical results.
作者
李海侠
Li Haixia(Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Shanxi Baoji 721013)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2017年第6期1094-1104,共11页
Acta Mathematica Scientia
基金
国家自然科学基金(11401356
11501496)
陕西省教育厅专项(16JK1046)
陕西省自然科学基础研究计划(2015JM1008)
博士后科学基金(2016M602767)~~
