Dynamics Study Of The Lotka-Volterra Reaction-diffusion Advection Model

This paper,on the one hand,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 variation:one live in the heterogeneous environment,the other live in the homogeneous environment.In this paper,firstly,we show that in all cases,the species living in homogeneous environment can never wipe out its competitor.Secondly,for the species which live in heterogeneous environment,it always have more advantage than the other,i.e.it either wipes out the other or the two competitors coexist.It is proved that for fixed dispersal rates,when the strength of the advection is sufficiently strong,the two competitive species coexist.This is a remarkable different result with obtained by He and Ni recently.On the other hand,some species can be more "smart" for surviving,so they will escape from the environments which are good for their competitors.This paper also studies another model:one species which live in the heterogeneous environment have advection along environmental gradient,other which live in the homogeneous environment can escape from the environments which are good for its competitor.We can obtain that when the strength of the advection is larger than a constant and the rate of escaping for other species is sufficiently small or sufficiently large,the two species coexist.