Phase Synchronization between Several Interacting Processes from Univariate Data

N. B. Janson; A. G. Balanov; V. S. Anishchenko; P. V. E. McClintock

doi:10.1103/PhysRevLett.86.1749

Phase Synchronization between Several Interacting Processes from Univariate Data

N. B. Janson, A. G. Balanov, V. S. Anishchenko, and P. V. E. McClintock

Phys. Rev. Lett. 86, 1749 – Published 26 February 2001

Abstract

A novel approach is suggested for detecting the presence or absence of synchronization between two or three interacting processes with different time scales in univariate data. It is based on an angle-of-return-time map. A model is derived to describe analytically the behavior of angles for a periodic oscillator under weak periodic and quasiperiodic forcing. An explicit connection is demonstrated between the return angle and the phase of the external periodic forcing. The technique is tested on simulated nonstationary data and applied to human heart rate variability data.

Received 12 October 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.1749

Authors & Affiliations

N. B. Janson^1,2, A. G. Balanov^1,2, V. S. Anishchenko², and P. V. E. McClintock¹

¹Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
²Department of Physics, Saratov State University, Astrahanskaya 83, 410026, Saratov, Russia