数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 173-184.

• 论文 • 上一篇    下一篇

一类具有Lotka-Volterra竞争模型共存解的存在性与稳定性

袁海龙, 李艳玲   

  1. 陕西师范大学数学与信息科学学院 西安 710119
  • 收稿日期:2016-05-27 修回日期:2016-10-14 出版日期:2017-02-26 发布日期:2017-02-26
  • 通讯作者: 李艳玲 E-mail:yanlingl@snnu.edu.cn
  • 作者简介:袁海龙,E-mail:422055696@163.com
  • 基金资助:

    国家自然科学基金(11271236,61672021)

Existence and Stability of Coexistence States for a Lotka-Volterra Competition Model

Yuan Hailong, Li Yanling   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Received:2016-05-27 Revised:2016-10-14 Online:2017-02-26 Published:2017-02-26
  • Supported by:

    Supported by the NSFC (11271236, 61672021)

摘要:

该文讨论了在空间分布不均匀的环境下一类具有Lotka-Volterra二维竞争模型的共存解的存在性与稳定性.特别地,两个竞争物种被假设拥有不同的内禀增长率,不同的种内竞争系数和种间竞争系数.结果表明当扰动参数τ充分小时,该模型的动力学行为被一些函数所刻画.该文使用的数学方法包含Lyapunov-Schmidt分解法,谱理论和单调动力系统理论.

关键词: 竞争, 稳定性, 共存解

Abstract:

In this paper, we consider the existence and stability of coexistence states in a Lotka-Volterra competition model with spatial heterogeneity of the environment. In particular, the two competing species are assumed that they have the different strengths of resources, the different intraspecific competition rates and the different interspecific competition rates. It turns out that the dynamics of system are determined by some scalar functions for small parameter τ. Our mathematical approach is based on Lyapunov-Schmidt reduction technique, spectral theory and monotone dynamical system theory.

Key words: Competition, Stability, Coexistence states

中图分类号: 

  • O175.26