# American Institute of Mathematical Sciences

December  2018, 23(10): 4255-4266. doi: 10.3934/dcdsb.2018136

## Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources

 1 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 2 Institute for Mathematical Sciences, Renmin University of China, Beijing 100872, China

* Corresponding author

Received  September 2017 Revised  December 2017 Published  April 2018

Fund Project: The first author is supported by Shanghai Peak Subject Funding.

This paper mainly study the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient. In this model, the species are assumed to be identical except spatial resource distribution: heterogeneity vs homogeneity. It is shown that the species with heterogeneous resources distribution is always in a better position, that is, it can always invade when rare. The ratio of advection strength and diffusion rate of the species with heterogeneous distribution plays a crucial role in the dynamics behavior of the system. Some conditions of invasion, driving extinction, and coexistence are given in term of this ratio and the diffusion rate of its competitor.

Citation: Benlong Xu, Hongyan Jiang. Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4255-4266. doi: 10.3934/dcdsb.2018136
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