Global dynamics of a Lotka-Volterra competition-diffusion-advection system for small diffusion rates in heterogenous environment

• Main Authors: Jinyu Wei, Bin Liu
• Format: Article
• Language: English
• Published: AIMS Press 2021-04-01
• Series: Mathematical Biosciences and Engineering
• Subjects: competition-diffusion-advection; heterogenous environment; principal eigenvalue; global stability; coexistence steady state
• Online Access: http://www.aimspress.com/article/doi/10.3934/mbe.2021031?viewType=HTML

We investigate the global dynamics of a Lotka-Volterra competition-diffusion-advection system for small diffusion rates in heterogenous environment. Our result suggests that the sign of $\int_{0}^{L}(m_{1}-m_{2})e^{kx}dx$ plays a significant role in understanding the global dynamics. In addition, the limiting behavior of coexistence steady state is obtained when diffusion rates of two species tend to zero meanwhile.