Application of the 0–1 test for chaos to experimental data

A reliable and efficient method to distinguish between chaotic and non-chaotic behaviour in noise-contaminated, but essentially stationary and deter-ministic, time series data has far reaching applications. Recently, we proposed a new method for detecting chaos which applies directly to the time series data and does not require phase space reconstruction. To illustrate the effectiveness of the method for experimental data, we analyse data from a bipolar motor. The standard technique to distinguish between regular and chaotic dynamics in deterministic time series data is to calculate the maximal Lyapunov exponent [1, 7, 14]. In the case of physical and biological applications, where the underlying dynamics is unknown, phase space reconstruction [1, 7, 16, 19, 18] is a necessary first step to compute Lyapunov exponents. However, there are problems inherent in phase space reconstruction as discussed in detail in [6, 17]. Recently, we proposed a new method [9] to detect chaos which applies directly to the time series data and does not require phase space reconstruction. Moreover, the dimension and origin of the dynamical system are irrelevant. The input is the time series data and the output is zero or one depending on whether the dynamics is non-chaotic or chaotic. This zero-one test for chaos is equally applicable to maps, ordinary and partial differential equations, and generally to data sets arising from deterministic systems. Of utmost importance is the effectiveness of the method for experimenta