Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment

Pages: 953 - 969, Volume 36, Issue 2, February 2016      doi:10.3934/dcds.2016.36.953

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Yuan Lou - Institute for Mathematical Sciences, Renmin University of China, Haidian District, Beijing, 100872, China (email)
Dongmei Xiao - Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China (email)
Peng Zhou - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada (email)

Abstract: We study a two-species Lotka-Volterra competition model in an advective homogeneous environment. It is assumed that two species have the same population dynamics and diffusion rates but different advection rates. We show that if one competitor disperses by random diffusion only and the other assumes both random and directed movements, then the one without advection prevails. If two competitors are drifting along the same direction but with different advection rates, then the one with the smaller advection rate wins. Finally we prove that if the two competitors are drifting along the opposite direction, then two species will coexist. These results imply that the movement without advection in homogeneous environment is evolutionarily stable, as advection tends to move more individuals to the boundary of the habitat and thus cause the distribution of species mismatch with the resources which are evenly distributed in space.

Keywords:  Reaction-diffusion-advection, Lotka-Volterra competition, advective environment, stability, co-existence steady state.
Mathematics Subject Classification:  Primary: 35K57, 35K61; Secondary: 92D25.

Received: July 2014;      Available Online: August 2015.