A new method, employing one-dimensional time series, is proposed for diagnostics of the presence or absence of phase synchronization between several interacting self-sustained oscillators. The procedure is based on introducing a polar coordinate system into the residence time mapping and studying the angle dynamics in this system. The method is verified by application to realizations reflecting the dynamics of two and three interacting processes in the presence of noise.
Translated from Pis’ma v Zhurnal Tekhnichesko Ï Fiziki, Vol. 27, No. 23, 2001, pp. 16–24.