Phase Characterization in Experimental Chaotic Systems

Abstract

In this work we present and discuss a method for measuring the phase of chaotic systems. This method has as input a scalar time series and operates by estimating a fundamental frequency for short segments, or windows, along the whole extension of the signal. It minimizes the mean square error of fitting a sinusoidal function to the series segment. This approach does not require following the trajectory on the attractor, works well over a wide range of adjustable parameters, is of easy implementation, and is particularly appealing for experimental settings with single signal outputs since there is no need of attractor reconstruction. We demonstrate the applicability of this method on experimental time series obtained from two coupled Chua circuits.