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This study introduces novel algebraic transcript-based tools for analyzing coupled time series. A new similarity distance measure was found to outperform existing methods for detecting generalized synchronization.

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Area of Science:

  • Dynamical Systems and Time Series Analysis
  • Information Theory
  • Group Theory

Background:

  • Coupled time series analysis is crucial for understanding complex systems.
  • Algebraic representations, such as ordinal patterns (permutations), offer a structured way to analyze time series.
  • Existing transcript-based tools have limitations in capturing complex couplings.

Purpose of the Study:

  • To outline and compare existing entropic and algebraic transcript-based tools for coupled time series analysis.
  • To introduce a novel similarity distance for evaluating coupled time series.
  • To assess the performance of these tools in detecting generalized synchronization.

Main Methods:

  • Utilizing algebraic representations (group-valued time series) and their inherent group structure.
  • Applying transcript-based analysis, including entropic measures (entropy, divergence, statistical complexity, mutual information) and algebraic measures (order classes, Cayley distance, Kendall distance).
  • Developing and evaluating a new similarity distance based on the mean Kendall distance.

Main Results:

  • Existing entropic and algebraic tools were reviewed and compared.
  • The newly proposed similarity distance was introduced as a mean Kendall distance.
  • The similarity distance demonstrated superior performance in detecting generalized synchronization compared to other tested tools.

Conclusions:

  • Transcript-based methods provide valuable insights into coupled time series.
  • The novel similarity distance is a promising tool for analyzing coupled systems.
  • This approach enhances the detection of phenomena like generalized synchronization in complex systems.