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Detecting chaos in irregularly sampled time series.

¹Department of Astronomy and Physics, Lycoming College, Williamsport, Pennsylvania 17701, USA.

Chaos (Woodbury, N.Y.)

|October 5, 2013

Summary

This study presents a new algorithm to detect chaos in irregularly sampled time series data. It modifies an existing method by using the Lomb-Scargle Periodogram (LSP) for power spectrum analysis, enabling chaos detection in previously challenging datasets.

Area of Science:

* Nonlinear dynamics
* Time series analysis
* Data science

Background:

* Chaos detection algorithms typically require regularly sampled time series data.
* Existing methods, such as those using the Discrete Fourier Transform (DFT), are unsuitable for irregularly sampled data.
* Real-world data often exhibit irregular sampling, posing challenges for chaos detection.

Purpose of the Study:

* To develop a robust algorithm for detecting chaos in irregularly sampled time series.
* To adapt existing chaos detection techniques for non-uniform data.
* To introduce a novel method for analyzing power spectra to differentiate chaotic and non-chaotic behavior.

Main Methods:

* Modification of Wiebe and Virgin's chaos detection algorithm.

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* Replacement of the Discrete Fourier Transform (DFT) with the Lomb-Scargle Periodogram (LSP) for power spectrum computation.

* Development of a new power spectrum analysis technique for irregular time series.

Main Results:

* The proposed algorithm effectively detects chaos in irregularly sampled time series.
* The Lomb-Scargle Periodogram (LSP) proves capable of analyzing the frequency content of irregularly sampled data.
* The method was successfully validated on both simulated and real-world observational data (variable stars).

Conclusions:

* The developed algorithm provides a reliable method for chaos detection in irregularly sampled data.
* The Lomb-Scargle Periodogram (LSP) is a suitable tool for spectral analysis of non-uniformly sampled time series.
* This advancement expands the applicability of chaos detection to a wider range of real-world datasets.