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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 557-567.doi: 10.3969/j.issn.1005-3085.2015.04.009

• • 上一篇    下一篇

一类Leslie-Gower捕食食饵模型的分歧

李  瑞,   李艳玲   

  1. 陕西师范大学数学与信息科学学院，西安 710062
  • 收稿日期:2013-12-31 接受日期:2015-01-23 出版日期:2015-08-15 发布日期:2015-10-15
  • 通讯作者: 李艳玲 E-mail: yanlingl@snnu.edu.cn
  • 基金资助:
    国家自然科学基金 (11271236)；中央高校基本科研业务费专项资金 (GK201401004).

The Bifurcation of a Class of Leslie-Gower Predator-prey Models

LI Rui,   LI Yan-ling   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
  • Received:2013-12-31 Accepted:2015-01-23 Online:2015-08-15 Published:2015-10-15
  • Contact: Y. Li. E-mail address: yanlingl@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11271236); the Fundamental Research Funds for the Central Universities (GK201401004).

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摘要： 本文研究了一类具有扩散的Leslie-Gower模型．利用谱分析和稳定性理论得到了两个正常数平衡态的局部稳定性；利用最大值原理、Harnack不等式和能量积分的方法得到了正稳态解的上下界估计和非常数正解的存在性；利用单特征值分歧理论研究了系统发自两个正常数平衡态的解分支，得到了非常数正解的存在性；利用Hopf分歧理论，得到了在平衡解处Hopf分歧的存在性．

关键词: Leslie-Gower, 先验估计, 分歧理论

Abstract:

A Leslie-Gower model with diffusion under homogeneous Neumann boundary condition is investigated in this paper. Firstly, the local stability of the constant steady-state is obtained by using the theory of spectral analysis and stability; secondly, by using the maximum principle, Harnack inequalities and energy method, the estimate of the upper and positive lower bound and nonexistence of nonconstant positive steady-state solution are obtained; by further applying simple eigenvalue bifurcation theory, the local bifurcations from the two constant solu-tions and the existence of nonconstant steady-state are given; finally, the constant solution where Hopf bifurcation occurs is obtained by using Hopf bifurcation theory.

Key words: Leslie-Gower, a prior estimate, bifurcation theory

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