A new criterion to distinguish stochastic and deterministic time series with the Poincaŕ section and fractal dimension

Abstract

In this paper, we propose a new method for detecting regular behavior of time series: this method is based on the Poincaŕ section and the Higuchi fractal dimension. The new method aims to distinguish random signals from deterministic signals. In fact, our method provides a pattern for decision making about whether a signal is random or deterministic. We apply this method to different time series, such as chaotic signals, random signals, and periodic signals. We apply this method to examples from all types of route to chaotic signals. This method has also been applied to data about iris tissues. The results show that the new method can distinguish different types of signals. © 2009 American Institute of Physics.