Phase synchronization between several interacting processes from univariate data

A novel approach is suggested for detecting the presence or absence of sync hronization between two or three interacting processes with different time scales in univariate data. It is based on an angle-of-return-time map. A mo del is derived to describe analytically the behavior of angles for a period ic oscillator under weak periodic and quasiperiodic forcing. An explicit co nnection is demonstrated between the return angle and the phase of the: ext ernal periodic forcing. The technique is tested on simulated nonstationary data and applied to human heart rate variability data.