LOTKA-VOLTERRA COMPETITION SYSTEM WITH STRONG ADVECTION RATES

A two-species Lotka-Volterra competition model in a strong advective homogeneous environment is explored, modeled by a system of advection-reaction equations. It is assumed that the two species have the same population dynamics but different advection rates. It is shown that the two-dimensional Lotka-Volterra competition model with advection can be written as a three-dimensional dynamical system in traveling wave coordinates, which facilitates the complete derivation of explicit traveling wave solutions. In particular, standing waves arise even in the presence of strong advection provided the advection rates have opposite signs.