一类n-斑块Lotka-Volterra型竞争系统的定性分析

Qualitative Analysis for a Lotka-Volterra n-Patch Competition System

本文研究了扩散和竞争能力对n个斑块两个物种的Lotka-Volterra竞争系统的动力学行为的联合影响。主要利用单调动力系统理论等方法建立了半平凡稳态解和共存稳态解的渐近稳定性。此外,在论文中还引入了一种新的矩阵主特征值的定义。

In this paper, we investigate the joint effects of diffusion and competition ability on the dynamics of a n-patch two-species Lotka-Volterra competition system. The asymptotic stability of semi-trivial and coexistence steady states is established mainly by using the theory of monotone dynamical systems. Moreover, we point out that a new definition of principal eigenvalue of matrix is introduced in this paper.