Complexity-Entropy Analysis of Chaotic and Intermittent Fluctuations in Physical Systems

Abstract

Time series from chaotic and stochastic systems share properties which can make it hard to distinguish them from each other. The Complexity-Entropy analysis provides appropriate measures of entropy and complexity and representing the calculated values in the representation space, the Complexity-Entropy plane, have been shown to be able to distinguish between time series of stochastic and chaotic origin. Time series from stochastic and chaotic systems appear in different regions of the Complexity-Entropy plane. The Complexity-Entropy analysis is applied to stochastic and chaotic systems with known locations in the Complexity-Entropy plane to confirm the already established result that these processes occupy different regions of the Complexity-Entropy plane. For continuous-time models, the effect of discretization timestep through resampling of the time series is investigated. The result of this analysis shows that continuous-time models should be represented by curves in the Complexity-Entropy plane, rather than with specific points implied from the literature. Using the fractional Brownian motion process, the effects of trends in the time series is investigated. The time series is detrended using a running mean approach. The result shows that the Complexity-Entropy analysis can separate time series with trends and noise processes. The Complexity-Entropy analysis is then applied to the well-known filtered Poisson process with constant and Pareto distributed duration times. The results shows that the parameter which has the largest effect on the shape of the curve in the Complexity-Entropy plane is the pulse shape, and not the duration times of the pulses. The Complexity-Entropy analysis is then applied to Bak-Tang-Wiesenfeld models. The results support what is stated in the literature, that these models can be described by the fractional Brownian motion process.