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Mode-locking in coupled map lattices

R. Carretero-González·D. K. Arrowsmith·F. Vivaldi
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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.

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R. Carretero-González, D. K. Arrowsmith, F. Vivaldi. 1998-01-09. Mode-locking in coupled map lattices. https://doi.org/10.1016/s0167-2789(96)00271-0

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