Applicability of the permutation largest slope entropy to strange nonchaotic attractors

Abstract

We extend the permutation largest slope entropy (PLSE) to the detection of strange nonchaotic attractors (SNA). The initial time series derived from a quasi-periodically forced chaotic map is first transformed into a series of symbols using the order relation. These symbols are thereafter combined into m-length words to obtain quantized ordinal matrices (QOM). Finally, the PLSE is applied to the series of QOM for detecting changes in the behavior of the system. Simulation results show that the QOM transform allows to control the complexity of the time series, hence to reduce the entropy of tori and SNA and to increase that of chaotic motions. This result allows to highlight transitions between the three types of motions, thus showing a nonzero entropy for SNA which nevertheless is smaller than that of chaotic dynamics. The approach is effective for the detection of different routes to SNA from time series.