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Estimating covariant Lyapunov vectors from data.

Christoph Martin1, Nahal Sharafi1, Sarah Hallerberg1

  • 1Department of Mechanical Engineering and Production Management, Hamburg University of Applied Sciences, Berliner Tor 21, 20099 Hamburg, Germany.

Chaos (Woodbury, N.Y.)
|April 2, 2022
PubMed
Summary

We developed a new data-driven method to estimate covariant Lyapunov vectors, which predict critical transitions in dynamical systems. This approach works even for complex, high-dimensional data without needing system equations.

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Area of Science:

  • Dynamical Systems Theory
  • Nonlinear Dynamics
  • Data Science

Background:

  • Covariant Lyapunov vectors (CLVs) describe perturbation growth in dynamical systems.
  • CLVs are crucial for predicting critical transitions and extreme events.
  • Estimating CLVs from data is essential when system equations are unknown.

Purpose of the Study:

  • To propose a novel, purely data-driven method for estimating covariant Lyapunov vectors.
  • To enable CLV estimation from high-dimensional datasets.
  • To demonstrate the accuracy of the proposed method on various dynamical systems.

Main Methods:

  • A new algorithm for estimating covariant Lyapunov vectors directly from time-series data.
  • Application to both low- and high-dimensional dynamical systems.
  • Validation using datasets with dimensions up to 128.

Main Results:

  • The proposed data-driven approach accurately estimates covariant Lyapunov vectors.
  • The method is effective for both low- and high-dimensional systems.
  • Successful estimation from time series up to 128 dimensions.

Conclusions:

  • A robust, data-driven method for estimating covariant Lyapunov vectors has been developed.
  • This approach expands the applicability of CLVs to complex, high-dimensional systems.
  • The method provides a powerful tool for analyzing dynamical systems and predicting critical events from observational data.