Abstract
We consider the (traveling-wave-like) fronts which propagate with rational velocityp/q in a simple coupled map lattice for which the local map has two stable fixed points. We prove the uniqueness of such orbits up to time iterations, space translations, and permutations of the associated codes. A condition for their existence is also given, but it has to be checked in each case. We expect this condition to serve as a selection mechanism. The technique employed, the so-called (generalized) transfer matrix method, allows us to give explicit expressions for these solutions. These fronts are actually the observed orbits in the numerical simulations, as is shown with two examples: the case of velocity 1/2 and that of velocity 1.
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Fernandez, B., Raymond, L. Propagating fronts in a bistable coupled map lattice. J Stat Phys 86, 337–350 (1997). https://doi.org/10.1007/BF02180209
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DOI: https://doi.org/10.1007/BF02180209