Propagation of nonlocal dispersal competition model with seasonal succession

Abstract

The paper considers the dynamical behaviors of two competing species for the case of weak competition with nonlocal dispersal and seasonal succession. We first derive the existence and non-existence of traveling waves connecting the trivial equilibrium and the positive periodic solution by using the method of upper-lower solutions and the asymptotic fixed point theorem. Then we obtain the asymptotic spreading properties of the two competing species with compactly supported initial conditions. Our results demonstrate that a competitively weaker species with a faster spreading speed can drive a competitively stronger but slower-spreading species to extinction.