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Statistically relaxing to generating partitions for observed time-series data.
Michael Buhl1, Matthew B Kennel
1Institute For Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA. mbuhl@clack.ucsd.edu
Summary
We developed a new algorithm to create better symbolic representations of complex time series data. This method improves the accuracy of dynamical system analysis by avoiding topological issues in generating partitions.
Area of Science:
- Dynamical systems theory
- Time series analysis
- Symbolic dynamics
Background:
- Generating partitions are crucial for preserving dynamical information in symbolic representations of deterministic maps.
- Existing methods may struggle with topological degeneracies, limiting analytical accuracy.
Purpose of the Study:
- Introduce a novel relaxation algorithm for estimating generating partitions from observed dynamical time series.
- Optimize the avoidance of topological degeneracies, a key property of generating partitions.
Main Methods:
- Employ a nonequilibrium stochastic minimization algorithm to optimize an energy-like functional.
- Assign symbols to observed data points without arbitrary parametrization constraints.
- Develop a method to select generating partition solutions that encode low-order unstable periodic orbits.
Main Results:
- The algorithm successfully estimates approximations to generating partitions.
- Topological degeneracies are effectively minimized.
- The method allows for the enumeration of potential generating partition solutions.
Conclusions:
- The proposed relaxation algorithm provides a robust method for analyzing dynamical time series.
- This approach enhances the fidelity of symbolic representations for deterministic systems.
- The ability to select specific partitions aids in understanding underlying system dynamics and periodic behaviors.