DETECTING PHASE SYNCHRONIZATION IN NOISY SYSTEMS

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 irrespective of a relation betwe en the original time series, The level of dependence between the insta ntaneous phases is quantified by a statistical dependence parameter, w hich 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 date. Possible applications of the proposed me thod are demonstrated by using both numerically generated and real exp erimental data, namely solutions of two coupled Rossler systems, mamma lian cardio-respiratory data, and long-term recordings of surface atmo spheric temperature and sunspot numbers. (C) 1997 Elsevier Science B.V .