一类带B-D反应项的食物链模型正解的稳定性和惟一性

J4 ›› 2013, Vol. 48 ›› Issue (09): 103-110.

• 论文 • 上一篇

一类带B-D反应项的食物链模型正解的稳定性和惟一性

李海侠1,2,李艳玲1

1. 陕西师范大学数学与信息科学学院, 陕西西安 710062;
2. 宝鸡文理学院数学系, 陕西宝鸡 721013

收稿日期:2013-03-07 出版日期:2013-09-20 发布日期:2013-09-25
作者简介:李海侠(1977- ),女,博士生, 讲师,研究方向为偏微分方程计算及其可视化.Email:xiami0820@163.com
基金资助:
国家自然科学基金资助项目(10971124);陕西省科技之星资助项目(2011kjxx12);陕西省教育厅科研计划资助项目(12JK0856);中央高校基本科研业务费专项资金资助(GK2013 02025)

Stability and uniqueness of positive solutions for a food chain model with B-D functional response

LI Hai-xia1,2, LI Yan-ling1

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China

Received:2013-03-07 Online:2013-09-20 Published:2013-09-25

摘要/Abstract

摘要：

研究了一类带Beddington-DeAngelis反应项的食物链模型正解的稳定性和惟一性。给出了正解的先验估计以及正解存在的充分和必要条件, 并讨论了正解稳定性和惟一性的充分条件。最后运用数值模拟对理论分析进行了验证和补充。

关键词: 食物链模型;Beddington-DeAngelis反应函数;稳定性;惟一性;数值模拟

Abstract:

Stability and uniqueness of positive solutions for a food chain model with Beddington-DeAngelis functional response are discussed. The a prior estimates and the sufficient and necessary conditions for the existence of positive solutions are obtained. In addition, the sufficient conditions for the stability and uniqueness of positive solutions are investigated. Finally, we make some numerical simulations to verify and complement the theoretical analysis.

Key words: food chain model; Beddington-DeAngelis functional response; stability; uniqueness; numerical simulations

李海侠1,2,李艳玲1. 一类带B-D反应项的食物链模型正解的稳定性和惟一性[J]. J4, 2013, 48(09): 103-110.

LI Hai-xia1,2, LI Yan-ling1. Stability and uniqueness of positive solutions for a food chain model with B-D functional response[J]. J4, 2013, 48(09): 103-110.

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一类带B-D反应项的食物链模型正解的稳定性和惟一性

Stability and uniqueness of positive solutions for a food chain model with B-D functional response

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