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Detecting phase synchronization in noisy systems

Milan Palus
Institute of Computer Science, Academy of Sciences of the Czech Republic
Pod vodárenskou vezí 2, 182 07 Prague 8, Czech Republic; and
School of Mathematics, Queensland University of Technology
GPO Box 2434, Brisbane, Qld 4001, Australia


A quantitative method for automatic detection of phase synchronization in noisy experimental bivariate time series is proposed, based on the fact that instantaneous phases of phase-synchronized (sub)systems are mutually dependent in a specific way irrespectively of a relation between the original time series. The level of dependence between the instantaneous phases is quantified by a statistical dependence parameter, which also reflects the strength of the systems' phase synchronization. Ranges of the parameter values, for which the detection of the phase synchronization can be considered reliable, are estimated by using the technique of surrogate data. Possible applications of the proposed method are demonstrated by using both numerically generated and real experimental data, namely solutions of two coupled Roessler systems, mammalian cardio-respiratory data, and long-term recordings of surface atmospheric temperature and sunspot numbers.

Phys. Lett. A 235 (1997) 341-351

Milan Palus 1997