INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL

This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c* , the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions.Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.