EXTENDED SYMBOLIC DYNAMICS IN BISTABLE CML - EXISTENCE AND STABILITY OF FRONTS

We consider a diffusive coupled map lattice (CML) for which the local map is piecewise affine and has two stable fixed points. By introducin g a spatio-temporal coding, we prove the one-to-one correspondence bet ween the set of global orbits and the set of admissible codes. This re lationship is applied to the study of the (uniform) fronts' dynamics. It is shown that, for any given velocity in [-1, 1], there is a parame ter set for which the fronts with that velocity exist and their shape is unique. The dependence of the fronts' velocity on the local map's d iscontinuity is proved to be a Devil's staircase. Moreover, the linear stability of the global orbits which do not reach the discontinuity f ollows directly from our simple map. Far the fronts, this statement is improved and as a consequence, the velocity of all the propagating in terfaces is computed far any parameter. The fronts' are shown to be al so nonlinearly stable under some restrictions on the parameters. Actua lly, these restrictions follow from the co-existence of uniform fronts and non-uniformly travelling fronts for strong coupling. Finally, the se results are extended to some C-infinity local maps.