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SSPRC

This repository contains implementation of two algorithms STPDP and SSRPC. The implementation code for each algorithm can be found in STPDP.py and SSRPC.py, and examples of how to use them are available in demo.ipynb. Detailed explanations and theoretical backgrounds of the algorithms are provided in the paper

  • STPDP (Sum of Trend Power and Detrended Power) algorithm enables noise-robust estimation of the mean orbital period for ergodic time series data.

  • SSRPC (State Space Reconstruction with Principal Components) algorithm enables noise-robust state space reconstruction. By utilizing this algorithm, valid, consistent, and noise-robust estimation of maximal Lyapunov exponent is available.

The following figures show noise-robustness, which is the primary advantage of SSRPC. Despite a significant level of noise, the slope of linear region of the divergence graph which represents maximal Lyapunov exponent remains consistent, in contrast to the conventional method.

Environment

This repository requires NoLiTSA, Numpy, Scipy, Numba, Matplotlib, and Scikit-learn

  • NoLiTSA is included as a submodule in this repository. It will be automatically installed when you clone this repository using the command below.

    git clone --recursive https://github.com/Lee-Jun-Hyuk-37/SSRPC.git

  • For more information about NoLiTSA, refer here.

  • You can install all libraries except for NoLiTSA using pip or conda. By following the commands below, you can install all the necessary libraries at once.

    pip install -r requirements.txt

    or

    conda create --name SSRPC --file requirements.txt
conda activate SSRPC

Publication

Published in Chaos, Solitons & Fractals. Link

Acknowledgement

I appreciate M. Mannattil for wonderful Github repository, NoLiTSA
Thanks to co-authors Il Seung Park and Jooeun Ahn for their contributions to this study.