Traveling fronts for Fisher–KPP lattice equations in almost-periodic media

Abstract

This paper investigates the existence of almost-periodic traveling fronts for Fisher–KPP lattice equations in one-dimensional almost-periodic media. Using the Lyapunov exponent of the linearized operator near the unstable steady state, we give sufficient conditions for the existence of a minimal speed of traveling fronts. Furthermore, it is shown that almost-periodic traveling fronts share the same recurrence property as the structure of the media. As applications, we give some typical examples which have minimal speed, and the proof of this depends on a dynamical system approach to the almost-periodic Schrödinger operator.