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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 ›› 2017, Vol. 34 ›› Issue (5): 534-550.doi: 10.3969/j.issn.1005-3085.2017.05.008

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空间互异对Lotka-Volterra竞争模型的影响（英）

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:2015-12-22 接受日期:2016-06-06 出版日期:2017-10-15 发布日期:2017-12-15
  • 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;61672021;11501496)；中央高校基础研究基金(GK201302005)；陕西省自然科学基金研究(2014JM1003)；陕西科技新星计划(2015KJXX-21).

The Effects of Spatial Variation in Lotka-Volterra Competition-diffusion Model

YUAN Hai-long,   LI Yan-ling   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Received:2015-12-22 Accepted:2016-06-06 Online:2017-10-15 Published:2017-12-15
  • Contact: Y. Li. E-mail address: yanlingl@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11271236; 61672021; 11501496); the Fundamental Research Fund for the Central Universities (GK201302005); the Natural Science Foundation Research of Shannxi Province (2014JM1003); the Shaanxi New-star Plan of Science and Technology (2015KJXX-21).

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摘要： 本文讨论了在齐次Neumann边界条件下一类具有Lotka-Volterra的竞争模型．我们研究了两物种在拥有不同种间竞争能力情况下，空间互异对物种产生的影响．特别地，我们考虑了在弱竞争的条件下，一个物种资源分布分布不均匀，而另一个物种资源分布是均匀的且两物种具有不同的物种总资源．结果表明某些参数对模型起着非常重要的作用．我们研究了系统共存解的存在性和稳定性，进而在适当的条件下，我们建立了共存解的唯一性及共存解和半平凡解的全局动力学行为．进一步，我们讨论了共存解关于扩散的渐近行为．结果表明系统的动力学关于参数是非常复杂的．我们使用的方法包括谱分析和单调动力系统理论等．

关键词: 空间互异, 全局渐近稳定, 竞争, 共存态

Abstract: In this paper, a two-species Lotka-Volterra competition-diffusion model with homo-geneous Neumann boundary conditions is considered. The effect of spatial heterogeneity and spatial homogeneity of environment on two competing species and their different competition abilities are studied. In particular, we consider the distribution of resources is heterogeneous for one species but homogeneous for another species with the different total resources in the weak competition. It turns out to be that some parameters play very important roles in this model. The existence, the stability of coexistence state of system is considered, and hence the unique coexistence state and the globally asymptotically stable of the coexistence state of system, and any semi-trivial solution of system can be established under some suitable conditions. Moreover, some limiting behaviors of coexistence state as the dispersal rates are also studied. Our results show that the dynamics of system is very complicated for some general parameters. The proposed method of analysis is based on spectral analysis and monotone dynamical systems theory.

Key words: spatial variation, globally asymptotically stable, competition, coexistence states

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