Detecting phase synchronization in noisy data from coupled chaotic oscillators

Abstract

Two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise. The first is a neighborhood-based method which links time delay embedding with instantaneous phase estimation. The second adopts the local projection method as a preprocessing filter to noisy data. Both schemes utilize the state recurrence, an important feature of chaotic data. The proposed schemes are applied to data measured from two typical chaotic systems, i.e., the coupled Rössler systems and the coupled Lorenz systems, respectively. The results show that phase synchronization, which may be buried by noise, is detected even when the noise level is high. Moreover, the overestimation of the degree of phase synchronization, which may be introduced by the Hilbert transform combined with a traditional linear bandpass filter, can be avoided when the data are contaminated by only measurement noise.