The transition to chaotic phase synchronization

E. Mosekilde, J. L. Laugesen, Zh. T. Zhusubaliyev

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Abstract

The transition to chaotic phase synchronization for a periodically driven spiral-type chaotic oscillator is known to involve a dense set of saddle-node bifurcations. By following the synchronization transition through the cascade of period-doubling bifurcations in a forced Ro¨ssler system, this paper describes how these saddle-node bifurcations arise and how their characteristic cyclic organisation develops. We identify the cycles that are involved in the various saddle-node bifurcations and describe how the formation of multi-layered resonance cycles in the synchronization domain is related to the torus doubling bifurcations that take place outside this domain. By examining a physiology-based model of the blood flow regulation to the individual functional unit (nephron) of the kidney we demonstrate how a similar bifurcation structure may arise in this system as a response to a periodically varying arterial blood pressure. The paper finally discusses how an alternative transition to chaotic phase synchronization may occur in the mutual synchronization of two chaotically oscillating period-doubling systems.
Original languageEnglish
Title of host publicationAIP Conference Proceedings
PublisherAmerican Institute of Physics
Publication date2012
Pages276-296
ISBN (Print)978-0-7354-1075-6
DOIs
Publication statusPublished - 2012
EventLet's face chaos through nonlinear dynamics: 8th International Summer School/Conference - University of Maribor, Maribor, Slovenia
Duration: 26 Jun 201110 Jul 2011
Conference number: 8

Conference

ConferenceLet's face chaos through nonlinear dynamics
Number8
LocationUniversity of Maribor
CountrySlovenia
CityMaribor
Period26/06/201110/07/2011
SeriesA I P Conference Proceedings Series
ISSN0094-243X

Bibliographical note

© 2012 American Institute of Physics

Keywords

  • Chaotic phase synchronization
  • Torus-doubling
  • Multi-layered tori
  • Nephron autoregulation
  • Physiology-based modeling

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