 9995 R. CarreteroGonz\'alez
 Low dimensional travelling interfaces in coupled map lattices
(182K, 7 pages, RevTeX, 6 Postscript figures)
Apr 2, 99

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Abstract. We study the dynamics of the travelling interface arising from a bistable
piecewise linear oneway coupled map lattice. We show how the dynamics of theinterfacial sites, separating the two superstable phases of the local map,
is finite dimensional and equivalent to a toral map. The velocity of the
travelling interface corresponds to the rotation vector of the toral map. As
a consequence, a rational velocity of the travelling interface is subject to
modelocking with respect to the system parameters. We analytically compute
the Arnold's tongues where particular spatiotemporal periodic orbits exist.
The boundaries of the modelocked regions correspond to bordercollision
bifurcations of the toral map. By varying the system parameters it is
possible to increase the number of interfacial sites corresponding to a
bordercollision bifurcation of the interfacial attracting cycle. We finally
give some generalizations towards smooth coupled map lattices whose interface
dynamics is typically infinite dimensional.
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