Wave propagation in a two-dimensional lattice dynamical system with global interaction

Abstract

In this paper, we study the wave propagation in a two-dimensional lattice dynamical system with global interaction, which arises in the study of a single species population with two age classes and a fixed maturation period living in a two-dimensional spatial unbounded environment. We consider the monostable case and show that for any given admissible speed, all the wave profiles propagating toward a fixed direction have the same asymptotic behaviors when they approach the limiting states, and they are unique up to translation. Moreover, we prove that all the wave profiles remain strictly increasing in the propagation process.