One-dimensional dynamics for travelling fronts in coupled map lattices
chao-dyn
2009-10-31 v1 adap-org
Adaptation and Self-Organizing Systems
Chaotic Dynamics
Pattern Formation and Solitons
patt-sol
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.
Cite
@article{arxiv.chao-dyn/9904008,
title = {One-dimensional dynamics for travelling fronts in coupled map lattices},
author = {R. Carretero-González and D. K. Arrowsmith and F. Vivaldi},
journal= {arXiv preprint arXiv:chao-dyn/9904008},
year = {2009}
}
Comments
10 pages, RevTeX, 12 Postscript figures, submitted to Phy.Rev.E