On the global orbits in a bistable CML.

In an infinite one-dimensional coupled map lattice (CML) for which the local map is piecewise affine and bistable, we study the global orbits using a spatiotemporal coding introduced in a previous work. The set of all the fixed points is first considered. It is shown that, under some restrictions on the parameters, the latter is a Cantor set, and we introduce an order to study the fixed points' existence. This also involves the proof of the coexistence of propagating fronts and stationary structures. In the second part, we analyze the global orbits which occur for strong coupling using the splitting of the dynamics into two independent (sub-)lattices, and emphasize the description of various traveling structures. (c) 1997 American Institute of Physics.