Abstract:

This paper is concerned with the existence of periodic forced waves on a two-dimensional lattice for Lotka-Volterra cooperative systems with a shifting habitat. First, we prove the existence and uniqueness of solutions to the initial value problem for the Lotka-Volterra system and establish a comparison principle. Second, we construct a pair of upper and lower solutions of the Lotka-Volterra cooperative system and prove the existence of periodic forced waves consistent with the habitat movement velocity by monotone iteration technique and combining the upper and lower solution methods.

Key words: existence, periodic forced waves, Lotka-Volterra cooperative system, monotone iteration technique, upper and lower solutions