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

Jinyu Wei; Bin Liu; Jinyu Wei; Bin Liu

doi:10.3934/mbe.2021031

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 564-582. doi: 10.3934/mbe.2021031

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Research article

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

Jinyu Wei ¹,
Bin Liu ^{2
,
,}

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

Received: 20 September 2020 Accepted: 23 November 2020 Published: 14 December 2020

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.
- competition-diffusion-advection,
- heterogenous environment,
- principal eigenvalue,
- global stability,
- coexistence steady state
Citation: Jinyu Wei, Bin Liu. Global dynamics of a Lotka-Volterra competition-diffusion-advection system for small diffusion rates in heterogenous environment[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 564-582. doi: 10.3934/mbe.2021031

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Abstract

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.

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