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

Mathematical Biosciences and Engineering

Jinyu Wei¹  Bin Liu² 

[1] 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China;

关键词: competition-diffusion-advection;    heterogenous environment;    principal eigenvalue;    global stability;    coexistence steady state;   

DOI  :  10.3934/mbe.2021031

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown