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Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.

Janson, N. B. and Balanov, A. G. and Anishchenko, V. S. and McClintock, Peter V. E. (2002) Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory. Physical Review E, 65 (3). 036211. ISSN 1539-3755

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Abstract

A general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system, using one-dimensional time series only. It is based on the introduction of angles and radii of return times maps, and on studying the dynamics of the angles. An explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data. It is valid under conditions of weak forcing. This correspondence is confirmed numerically for a nonstationary process in a forced Van der Pol system. A model describing the angles’ behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived.

Item Type: Article
Journal or Publication Title: Physical Review E
Subjects: Q Science > QC Physics
Departments: Faculty of Science and Technology > Physics
ID Code: 31813
Deposited By: Professor P. V. E. McClintock
Deposited On: 18 Feb 2010 15:55
Refereed?: Yes
Published?: Published
Last Modified: 26 Jul 2012 17:01
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/31813

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