一类具有Lotka-Volterra竞争模型共存解的存在性与稳定性

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

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Υ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.

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 7. Our mathematical approach is based on Lyapunov-Schmidt reduction technique, spectral theory and monotone dynamical system theory.