The transition to chaotic phase synchronization

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

doi:10.1063/1.4745590

The transition to chaotic phase synchronization

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

Department of Physics

Southwest State University

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

368 Downloads (Pure)

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 language	English
Title of host publication	AIP Conference Proceedings
Publisher	American Institute of Physics
Publication date	2012
Pages	276-296
ISBN (Print)	978-0-7354-1075-6
DOIs	https://doi.org/10.1063/1.4745590
Publication status	Published - 2012
Event	Let's face chaos through nonlinear dynamics: 8th International Summer School/Conference - University of Maribor, Maribor, Slovenia Duration: 26 Jun 2011 → 10 Jul 2011 Conference number: 8

Conference

Conference	Let's face chaos through nonlinear dynamics
Number	8
Location	University of Maribor
Country/Territory	Slovenia
City	Maribor
Period	26/06/2011 → 10/07/2011

Series	A I P Conference Proceedings Series
ISSN	0094-243X

Bibliographical note

Keywords

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

Access to Document

10.1063/1.4745590

APC000276Final published version, 2.03 MB

OpenUrl availability

Full text

Cite this

@inproceedings{ea345ee13c244688913bddd5aa4b8676,

title = "The transition to chaotic phase synchronization",

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.",

keywords = "Chaotic phase synchronization, Torus-doubling, Multi-layered tori, Nephron autoregulation, Physiology-based modeling",

author = "E. Mosekilde and Laugesen, {J. L.} and Zhusubaliyev, {Zh. T.}",

note = "{\textcopyright} 2012 American Institute of Physics; Let's face chaos through nonlinear dynamics : 8th International Summer School/Conference ; Conference date: 26-06-2011 Through 10-07-2011",

year = "2012",

doi = "10.1063/1.4745590",

language = "English",

isbn = "978-0-7354-1075-6",

series = "A I P Conference Proceedings Series",

publisher = "American Institute of Physics",

pages = "276--296",

booktitle = "AIP Conference Proceedings",

}

TY - GEN

T1 - The transition to chaotic phase synchronization

AU - Mosekilde, E.

AU - Laugesen, J. L.

AU - Zhusubaliyev, Zh. T.

N1 - Conference code: 8

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Chaotic phase synchronization

KW - Torus-doubling

KW - Multi-layered tori

KW - Nephron autoregulation

KW - Physiology-based modeling

U2 - 10.1063/1.4745590

DO - 10.1063/1.4745590

M3 - Article in proceedings

SN - 978-0-7354-1075-6

T3 - A I P Conference Proceedings Series

SP - 276

EP - 296

BT - AIP Conference Proceedings

PB - American Institute of Physics

T2 - Let's face chaos through nonlinear dynamics

Y2 - 26 June 2011 through 10 July 2011

ER -

The transition to chaotic phase synchronization

Abstract

Conference

Bibliographical note

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this