Propagation dynamics of forced pulsating waves of a time periodic Lotka-Volterra competition system in a shifting habitat

Abstract

Existence, uniqueness and stability of forced pulsating waves as well as gap formation of reaction diffusion models in a shifting habitat are challenging problems in the field of propagation dynamics. In this paper, we design to tackle these problems for a time periodic Lotka-Volterra competition system. By using alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating traveling wave, as long as the shifting speed falls in a finite interval where the end points are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating traveling wave are derived and this helps us show that this wave is unique. Moreover in the Lyapunov sense, the stability of the forced pulsating wave is also studied. Finally, when the forced speed is beyond the finite interval, gap formation is investigated theoretically and illustrated further by numerical simulations.