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Orbital decomposition for ill-behaved event sequences: transients and superordinate structures.

Stephen J Guastello1, Anthony F Peressini, Robert W Bond

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Transient functions in time series data can be analyzed using orbital decomposition. This method, based on coupled oscillators, helps identify patterns in chaotic series and real-world event data.

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Area of Science:

  • Complex systems analysis
  • Nonlinear dynamics
  • Time series analysis

Background:

  • Transient functions pose challenges in time series analysis.
  • Symbolic dynamics and orbital decomposition offer methods to study complex temporal patterns.
  • Chaotic series are theorized to originate from coupled oscillators.

Purpose of the Study:

  • To investigate the impact of various transient functions on time series analysis using orbital decomposition.
  • To assess the applicability of orbital decomposition to real-world, potentially non-ergodic datasets.
  • To explore the relationship between transient events and the underlying dynamics of chaotic systems.

Main Methods:

  • Orbital decomposition, a symbolic dynamics technique, was employed.
  • Synthetic time series data were generated to simulate intrusive events, merged functions, non-coupled oscillators, and driving oscillations.
  • Real-world datasets, including patient ritual behaviors (obsessive-compulsive disorder) and serial murder event timings, were analyzed.

Main Results:

  • The study identified how different types of transients influence the statistical patterns derived from orbital decomposition.
  • Synthetic data revealed distinct signatures for various transient phenomena.
  • Real-world data exhibited non-ergodic properties consistent with findings from synthetic datasets.

Conclusions:

  • Orbital decomposition is a viable method for analyzing transient functions in time series data.
  • The presence of coupled oscillators and specific transient events can be inferred from time series patterns.
  • This approach offers insights into complex behaviors in both artificial and natural systems.