Bichromatic travelling waves for lattice Nagumo equations

TL;DR

This paper investigates bichromatic front solutions in lattice Nagumo equations, revealing conditions for their movement and how they enable coexistence and spreading of stable states through periodic patterns.

Contribution

It provides explicit criteria for the existence and mobility of bichromatic fronts, extending understanding beyond standard monochromatic solutions in lattice Nagumo equations.

Findings

Bichromatic fronts can be stationary or traveling depending on parameters.

These fronts connect homogeneous and 2-periodic equilibria.

Bichromatic waves facilitate coexistence and spreading of stable states.

Abstract

We discuss bichromatic (two-color) front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatially heterogeneous 2-periodic equilibria and hence are not monotonic like the standard monochromatic fronts. We provide explicit criteria that can determine whether or not these fronts are stationary and show that the bichromatic fronts can travel in parameter regimes where the monochromatic fronts are pinned. The presence of these bichromatic waves allows the two stable homogeneous equlibria to both spread out through the spatial domain towards each other, buffered by a shrinking intermediate zone in which the periodic pattern is visible.