Mode-locking in coupled map lattices

Abstract

We study propagation of pulses along one-way coupled map lattices, which originate from the transition between two superstable states of the local map. The velocity of the pulses exhibits a staircase-like behaviour as the coupling parameter is varied. For a piece-wise linear local map, we prove that the velocity of the wave has a Devil's staircase dependence on the coupling parameter. A wave travelling with rational velocity is found to be stable to parametric perturbations in a manner akin to rational mode-locking for circle maps. We provide evidence that mode-locking is also present for a broader range of maps and couplings.

11 TeX pages + 2 PostScript pages with 10 figures

References in corpus (2)

• Chaotic Traveling Waves in a Coupled Map Lattice
• Existence and Stability of Steady Fronts in Bistable CML

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• Scaling properties of invariant densities of coupled Tchebyscheff maps
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• Pinned, locked, pushed, and pulled traveling waves in structured environments
• Low dimensional travelling interfaces in coupled map lattices
• A first approach to the Galois group of chaotic chains