Dynamical behavior for a Lotka-Volterra weak competition system in advective homogeneous environment

De Tang

doi:10.3934/dcdsb.2019037

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2019, Volume 24, Issue 9: 4913-4928. Doi: 10.3934/dcdsb.2019037

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Dynamical behavior for a Lotka-Volterra weak competition system in advective homogeneous environment

De Tang^,

School of Mathematics(Zhuhai), Sun Yat-sen University, Zhuhai 519082, Guangdong, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2018

Revised: June 30, 2018

Early access: February 2019

Published: July 2019

The author is supported by NSF grant 11801089, Postdoctoral Science Foundation of China(N0.2018M643281)

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Abstract

We consider a two-species Lotka-Volterra weak competition model in a one-dimensional advective homogeneous environment, where individuals are exposed to unidirectional flow. It is assumed that two species have the same population dynamics but different diffusion rates, advection rates and intensities of competition. We study the following useful scenarios: (1) if one species disperses by random diffusion only and the other assumes both random and unidirectional movements, two species will coexist; (2) if two species are drifting along the different direction, two species will coexist; (3) if the intensities of inter-specific competition are small enough, two species will coexist; (4) if the intensities of inter-specific competition are close to 1, the competitive exclusion principle holds. These results provide a new mechanism for the coexistence of competing species. Finally, we apply a perturbation argument to illustrate that two species will converge to the unique coexistence steady state.

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Mathematics Subject Classification: Primary: 35K57, 35B32; Secondary: 92D25.

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