中文摘要：

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.

英文摘要：

In this paper, a two-species Lotka-Volterra competition-diffusion model with homogeneous 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.