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This study introduces data-driven phase and isostable coordinates for analyzing complex dynamical systems. This method simplifies high-dimensional models using only observed data, enabling analysis of systems with unknown equations.

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Area of Science:

  • Dynamical Systems Theory
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Phase-amplitude reduction is crucial for analyzing oscillatory systems.
  • Existing methods struggle with experimental data and unknown equations.
  • Amplitude coordinates offer richer descriptions of transient dynamics.

Purpose of the Study:

  • Develop a data-driven framework for phase-amplitude reduction.
  • Infer reduced models from observed system output.
  • Create data-driven phase and isostable coordinates for unknown systems.

Main Methods:

  • Utilize proper orthogonal reduction to identify transient decay features.
  • Relate identified features to existing phase and isostable coordinates.
  • Define new data-driven coordinates valid across the limit cycle's basin of attraction.

Main Results:

  • Successfully inferred phase-amplitude reduced models from observed data.
  • Demonstrated the utility of data-driven coordinates in neural physiology examples.
  • Enabled computationally intractable optimal control strategies.

Conclusions:

  • The proposed framework provides a powerful tool for analyzing nonlinear dynamical systems with unknown or complex equations.
  • Data-driven phase and isostable coordinates are valuable for high-dimensional and experimental systems.
  • This approach overcomes limitations of traditional phase-amplitude reduction techniques.