Coexistence in a competition-diffusion-advection system with equal amount of total resources

Jinyu Wei; Bin Liu; Jinyu Wei; Bin Liu

doi:10.3934/mbe.2021178

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3543-3558. doi: 10.3934/mbe.2021178

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Research article

Coexistence in a competition-diffusion-advection system with equal amount of total resources

Jinyu Wei ^1,2,
Bin Liu ^{1,2
,
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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: 14 January 2021 Accepted: 18 April 2021 Published: 23 April 2021

We consider a Lotka-Volterra competition-diffusion-advection system with the total resources for two competitors fixed at the same level. We reveal the combined effect of competition abilities and spatial variations on the coexistence of two competing species. It is obtained that when the ratio of advection rate $ \alpha $ to diffusion rate $ d_1 $ is appropriately large, the two competing species will always coexist if the inter-specific competition coefficients $ (b, c) $ in $ (0, 1]\times(0, 1] $ and when the ratio is appropriately small, the two species will coexist if the inter-specific competition coefficients $ c $ is appropriately small and $ b $ is in $ (0, 1] $.
- competition-diffusion-advection,
- coexistence,
- linearly stable,
- principle eigenvalue,
- monotone dynamical system
Citation: Jinyu Wei, Bin Liu. Coexistence in a competition-diffusion-advection system with equal amount of total resources[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3543-3558. doi: 10.3934/mbe.2021178

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Abstract

We consider a Lotka-Volterra competition-diffusion-advection system with the total resources for two competitors fixed at the same level. We reveal the combined effect of competition abilities and spatial variations on the coexistence of two competing species. It is obtained that when the ratio of advection rate $ \alpha $ to diffusion rate $ d_1 $ is appropriately large, the two competing species will always coexist if the inter-specific competition coefficients $ (b, c) $ in $ (0, 1]\times(0, 1] $ and when the ratio is appropriately small, the two species will coexist if the inter-specific competition coefficients $ c $ is appropriately small and $ b $ is in $ (0, 1] $.

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