Non-transitive maps in phase synchronization

Murilo Da Silva Baptista, T. Pereira, J. C. Sartorelli, I. L. Caldas, Jurgen Kurths

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)216-232
Number of pages17
JournalPhysica. D, Nonlinear Phenomena
Issue number3-4
Publication statusPublished - 15 Dec 2005


  • chaotic phase synchronization
  • ergodic theory
  • temporal mappings
  • kicked logistic map
  • chaotic oscillators


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