一类食物链模型正解的稳定性和唯一性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (6): 1094-1104.

一类食物链模型正解的稳定性和唯一性

李海侠

宝鸡文理学院数学与信息科学学院陕西宝鸡 721013

收稿日期:2016-10-24 修回日期:2017-03-14 出版日期:2017-12-26 发布日期:2017-12-26
作者简介:李海侠,E-mail:xiami0820@163.com
基金资助:
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）和博士后科学基金（2016M602767）

Stability and Uniqueness of Positive Solutions for a Food-Chain Model

Li Haixia

Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Shanxi Baoji 721013

Received:2016-10-24 Revised:2017-03-14 Online:2017-12-26 Published:2017-12-26
Supported by:
Supported by the NSFC (11401356, 11501496), the Foundations of Shaanxi Educational Committee (16JK1046), the Natural Science Basic Research Plan in Shaanxi Province of China (2015JM1008) and the Postdoctoral Science Foundation of China (2016M602767)

摘要/Abstract

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.

关键词: 食物链模型, Crowley-Martin反应函数, 不动点指数, 稳定性, 唯一性

Abstract: 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.

Key words: Food-chain model, Crowley-Martin functional response, Fixed point index, Stability, Uniqueness

中图分类号:

O175.26

李海侠. 一类食物链模型正解的稳定性和唯一性[J]. 数学物理学报, 2017, 37(6): 1094-1104.

Li Haixia. Stability and Uniqueness of Positive Solutions for a Food-Chain Model[J]. Acta mathematica scientia,Series A, 2017, 37(6): 1094-1104.

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