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

TL;DR

This paper studies the existence and properties of almost periodic traveling fronts in Fisher-KPP lattice equations within almost periodic media, linking minimal speed conditions to Lyapunov exponents and media recurrence properties.

Contribution

It provides new sufficient conditions for the existence of minimal speed traveling fronts in almost periodic media using Lyapunov exponents and dynamical systems methods.

Findings

Existence of almost periodic traveling fronts under certain Lyapunov exponent conditions

Traveling fronts share the recurrence properties of the media

Examples demonstrating minimal speed traveling fronts

Abstract

This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the linearized operator near the unstable steady state, we give sufficient condition of the existence of minimal speed of traveling fronts. Furthermore, it is showed 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 dynamical system approach to almost periodic Schrodinger operator.