Selective chaos of travelling waves in feedforward chains of bistable maps

Abstract

We study the chaos of travelling waves (TW) in unidirectional chains of bistable maps. Previous numerical results suggested that this property is selective, {\sl viz.}\ given the parameters, there is at most a single (non-trivial) velocity for which the corresponding set of wave profiles has positive topological entropy. However, mathematical proofs have remained elusive, in particular because the related symbolic dynamics involves entire past sequences. Here, we consider instead inite (short) rank approximations for which the symbolic dynamics has finite memory. For every possible velocity, we compute the existence domains of all possible finite type subshifts of TW with positive entropy. In all examples, chaos of TW turns out to be selective, indeed.