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Uncovering interaction of coupled oscillators from data
Björn Kralemann1, Laura Cimponeriu, Michael Rosenblum
1Department of Physics, University of Potsdam, Postfach 601553, D-14415 Potsdam, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
Summary
This study introduces a novel method to reconstruct phase dynamics equations for coupled oscillators using observational data. The technique allows for an invariant description of oscillator behavior and recovery of natural frequencies.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Data-Driven Modeling
Background:
- Understanding the dynamics of coupled oscillatory systems is crucial in various scientific fields.
- Reconstructing governing equations from observational data presents significant challenges, especially for phase dynamics.
Purpose of the Study:
- To develop a general technique for reconstructing phase dynamics equations of weakly coupled oscillators from scalar observational data.
- To achieve an invariant description of phase dynamics, independent of specific observable choices.
- To demonstrate the recovery of intrinsic oscillator properties, such as natural frequencies.
Main Methods:
- Reconstruction of dynamics in terms of protophases from general scalar observables.
- Transformation to observable-independent phases for an invariant description.
- Utilizing multiple observations across different coupling strengths to identify natural frequencies.
Main Results:
- A systematic method for deriving phase dynamics equations from time-series data was established.
- The approach yields an invariant representation of the phase dynamics, robust to the choice of observables.
- Natural frequencies of individual oscillators were successfully recovered under specific experimental conditions.
Conclusions:
- The developed technique provides a powerful tool for analyzing and understanding complex oscillatory systems from empirical data.
- The method offers a pathway to uncover fundamental properties of coupled oscillators, including their intrinsic frequencies.
- Successful application to both numerical simulations and a physical experiment with coupled metronomes validates the theory.
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