R. Carretero-Gonz\'alez, D.K. Arrowsmith, F. Vivaldi
One-dimensional dynamics for travelling fronts in coupled map lattices
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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.