Detecting Nonlinearity and Edge-of-Chaos Phenomena in Ordinal Data

Rachel Heath, University of Newcastle, Australia

Abstract: Some but not all algorithms for detecting nonlinearity in experimental data, such as prediction methods and Lyapunov spectra, require a much larger amount of stable continuous data than is generally available from individual human participants. A new method for detecting nonlinearity in relatively short data sets, Monotonic Ectropy, computes the change in Shannon information as ordinal scale values evolve over time by comparing runs of various lengths and directions. This method compares two successive ordinal scale changes with similar monotonic changes for three successive ordinal scale values. The resulting index discriminates a chaotic Henon series from both Gaussian noise and phase-randomised surrogate series, the latter containing the stochastic structure of the Henon series but without the nonlinearity. The empirical utility of the technique is illustrated using mood rating data obtained from two participants, one suffering from chronic depression, the other showing no signs of the disorder. Although Monotonic Ectropy discriminated between the mood ratings of the depressed and nondepressed subjects, evidence for nonlinearity was only obtained using Lempel-Ziv complexity, a measure based on symbolic dynamics. This was probably due to Monotonic Ectropy”s unique sensitivity to edge-of-chaos phenomena.

Keywords: entropy, symbolic dynamics, mood ratings, order, depression, complexity