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Non-trivial collective behavior in coupled map lattices: A transfer operator perspective

par Chaté, Hugues;Losson, Jérôme
Référence Physica. D, 103, 1-4, page (51-72)
Publication Publié, 1997

Article révisé par les pairs

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Résumé :

We discuss the link between the presence of non-trivial collective behavior in coupled map lattices, and the spectral properties of their transfer (or Perron-Frobenius) operator. In particular, it is argued that non-trivial collective behavior corresponds to a Perron-Frobenius operator possessing a cyclical spectral decomposition known as asymptotic periodicity. We also discuss to what extent changes in the spectral properties of the Perron-Frobenius operator are related to the phase transitions observed between two types of non-trivial collective behavior. Copyright © 1997 Elsevier Science B.V. All rights reserved.