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Estimating Phase From Observed Trajectories Using the Temporal 1-Form.

Simon Wilshin1, Matthew D Kvalheim2, Clayton Scott3

  • 1Royal Vet College, London NW1 OTU, UK swilshin@rvc.ac.uk.

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Summary
This summary is machine-generated.

This study introduces a novel algorithm to estimate the asymptotic phase of oscillators using a series expansion. This method accurately recovers phase response curves (PRCs) and oscillator dynamics from short time-series data.

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Area of Science:

  • Dynamical Systems
  • Nonlinear Dynamics
  • Time Series Analysis

Background:

  • Oscillators are fundamental in nature, with dynamics often dictated by an asymptotic phase.
  • Existing data-driven methods for phase estimation can be limited by data length and noise sensitivity.

Purpose of the Study:

  • To develop a robust algorithm for estimating the asymptotic phase of oscillators.
  • To enable accurate recovery of phase response curves (PRCs) and isochron geometry from time-series data.

Main Methods:

  • A novel series expansion is employed to directly compute the phase response curve (PRC).
  • An algorithm is provided for estimating the coefficients of this series expansion.
  • The method is designed to handle short observations and varying noise conditions.

Main Results:

  • The algorithm accurately estimates asymptotic phase even with data shorter than one cycle.
  • Proven convergence rate bounds are established concerning measurement and system noise.
  • The method successfully recovers PRCs, isochron curvature, and nonlinear geometric features.

Conclusions:

  • This data-driven approach offers a powerful tool for modeling oscillator dynamics from observed time-series.
  • The algorithm's ability to use short data segments and its noise resilience make it broadly applicable.
  • Potential applications include constructing oscillator models in diverse scientific and engineering fields.