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Non-transitive maps in phase synchronization

  • Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved

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Author:Murilo S. Baptista, Tiago Pereira, J. C. Sartorelli, I. L. Caldas, Jürgen KurthsORCiDGND
Document Type:Article
Year of first Publication:2005
Year of Completion:2005
Release Date:2017/03/24
Source:Physica / d. - 212 (2005), 3-4, S. 216 - 232
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik