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

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Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory. / Janson, N. B.; Balanov, A. G.; Anishchenko, V. S. et al.
In: Physical Review E, Vol. 65, No. 3, 15.02.2002, p. 036211.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Janson, NB, Balanov, AG, Anishchenko, VS & McClintock, PVE 2002, 'Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.', Physical Review E, vol. 65, no. 3, pp. 036211. https://doi.org/10.1103/PhysRevE.65.036211

APA

Janson, N. B., Balanov, A. G., Anishchenko, V. S., & McClintock, P. 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. https://doi.org/10.1103/PhysRevE.65.036211

Vancouver

Janson NB, Balanov AG, Anishchenko VS, McClintock PVE. Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory. Physical Review E. 2002 Feb 15;65(3):036211. doi: 10.1103/PhysRevE.65.036211

Author

Janson, N. B. ; Balanov, A. G. ; Anishchenko, V. S. et al. / Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory. In: Physical Review E. 2002 ; Vol. 65, No. 3. pp. 036211.

Bibtex

@article{ed6e37472e9546de81a568d77b4feca7,
title = "Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.",
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{\textquoteright} behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived.",
author = "Janson, {N. B.} and Balanov, {A. G.} and Anishchenko, {V. S.} and McClintock, {Peter V. E.}",
year = "2002",
month = feb,
day = "15",
doi = "10.1103/PhysRevE.65.036211",
language = "English",
volume = "65",
pages = "036211",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "3",

}

RIS

TY - JOUR

T1 - Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.

AU - Janson, N. B.

AU - Balanov, A. G.

AU - Anishchenko, V. S.

AU - McClintock, Peter V. E.

PY - 2002/2/15

Y1 - 2002/2/15

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.65.036211

DO - 10.1103/PhysRevE.65.036211

M3 - Journal article

VL - 65

SP - 036211

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 3

ER -