Abstract
To detect coupling between two oscillators from a time series, we suggest a method based on the estimation of the phase increments correlation with an analytic test for significance. With exemplary oscillators, we show that the suggested method complements a widely used approach based on the estimation of the mean phase coherence. In particular, the suggested method allows efficient detection of a non-synchronizing coupling and, due to a less restrictive null hypothesis, it is applicable to a wider range of situations, including arbitrarily strong phase nonlinearities.
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References
A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization: A universal concept in nonlinear sciences (Cambridge University Press, Cambridge, 2001)
V.S. Anishchenko, V.V. Astakhov, A.B. Neiman, N.E. Vadivasova, L. Schimanski-Geier, Nonlinear dynamics of chaotic and stochastic systems (Springer-Verlag, Berlin, 2002)
E. Mosekilde, Yu. Maistrenko, D. Postnov, Chaotic synchronization: Applications to living systems (World Scientific, Singapore, 2002)
S. Boccaletti, J. Kurths, G. Osipov, D. Valladares, C. Zhou, Phys. Rep. 366, 1 (2002)
G.V. Osipov, J. Kurths, C. Zhou, Synchronization in oscillatory networks (Springer-Verlag, Berlin, 2007)
A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva, Synchronization: From simple to complex (Springer-Verlag, Berlin, 2008)
F. Mormann, K. Lehnertz, P. David, C.E. Elger, Physica D 144, 358 (2000)
M.G. Rosenblum, A.S. Pikovsky, J. Kurths, C. Schaefer, P.A. Tass, in Neuro-informatics, edited by F. Moss and S. Gielen, Handbook of Biological Physics 4 (Elsevier Science, New York, 2000), p. 279
A. Kraskov, T. Kreuz, R. Quian Quiroga, P. Grassberger, F. Mormann, K. Lehnertz, C.E. Elger, Epilepsia 43, 48 (2002)
M.D. Prokhorov, V.I. Ponomarenko, V.I. Gridnev, M.B. Bodrov, A.B. Bespyatov, Phys. Rev. E 68, 041913 (2003)
A.Ye. Hramov, A.A. Koronovskii, Chaos 14, 603 (2004)
A.N. Pavlov, O.V. Sosnovtseva, O.N. Pavlova, E. Mosekilde, N.-H. Holstein-Rathlou, Physiol. Meas. 29, 945 (2008)
A.S. Karavaev, M.D. Prokhorov, V.I. Ponomarenko, A.R. Kiselev, V.I. Gridnev, E.I. Ruban, B.P. Bezruchko, Chaos 19, 033112 (2009)
D.A. Smirnov, U.B. Barnikol, T.T. Barnikol, B.P. Bezruchko, C. Hauptmann, C. Buehrle, M. Maarouf, V. Sturm, H.-J. Freund, P.A. Tass, Europhys. Lett. 83, 20003 (2008)
I.I. Mokhov, D.A. Smirnov, Geophys. Res. Lett. 33, L03708 (2006)
B.P. Bezruchko, D.A. Smirnov, Extracting knowledge from time series: An introduction to nonlinear empirical modeling (Springer-Verlag, Berlin, 2010)
C. Allefeld, J. Kurths, Int. J. Bif. Chaos 14, 405 (2004)
B. Schelter, M. Winterhalder, J. Timmer, M. Peifer, Phys. Lett. A 366, 382 (2007)
J. Brea, D.F. Russell, A.B. Neiman, Chaos 16, 026111 (2006)
D.A. Smirnov, E.V. Sidak, B.P. Bezruchko, Sov. Tech. Phys. Lett. 39, 40 (2013)
P.A. Tass, Phase resetting in medicine and biology. Stochastic modelling and data analysis (Springer-Verlag, Berlin, 1999)
A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Int. J. Bifurc. Chaos 10, 2291 (2000)
A.A. Borovkov, Mathematical statistics (Fizmatlit, Moscow, 2007)
G.E.P. Box, G.M. Jenkins, Time series analysis. Forecasting and control (Holden-Day, San Francisco, 1970)
B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Phys. Rev. E 77, 066205 (2008)
V.S. Anishenko, T.Ye. Vadivasova, G.A. Okrokvertskhov, G.I. Strelkova, Physics – Uspekhi 175, 163 (2005)
V.V. Matrosov, V.D. Shalfeev, Dynamical chaos in phase systems. A tutorial (Nizhny Novgorod State University, Nizhny Novgorod, 2007)
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Smirnov, D., Sidak, E. & Bezruchko, B. Detection of coupling between oscillators with analytic tests for significance. Eur. Phys. J. Spec. Top. 222, 2441–2451 (2013). https://doi.org/10.1140/epjst/e2013-02028-5
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DOI: https://doi.org/10.1140/epjst/e2013-02028-5