PROPAGATION DYNAMICS OF FORCED PULSATING WAVES OF A TIME PERIODIC LOTKA-VOLTERRA COOPERATIVE SYSTEM WITH NONLOCAL DIFFUSION IN SHIFTING

In this paper, we will concern the existence, asymptotics and stability of forced pulsating waves in a Lotka-Volterra cooperative system with nonlocal diffusion under shifting habitats. By using alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves for any given positive speed of the shifting habitat. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial value, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.