One-dimensional dynamics for travelling fronts in coupled map lattices

Abstract

Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional dynamics to a one-dimensional circle homeomorphism, whose rotation number gives the propagation velocity. The mode-locking of the velocity with respect to the system parameters then typically follows. We study the behaviour of fronts near the boundary of parametric stability, and we explain how the mode-locking tends to disappear as we approach the continuum limit of an infinite density of sites.