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Anticipating synchrony in dynamical systems using information theory.

Anupam Ghosh1, Samadhan A Pawar1, R I Sujith1

  • 1Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India.

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Summary

This study introduces a new information theory measure (R) to predict harmful synchronization in coupled dynamical systems. This early warning system is crucial for applications where synchronization can be detrimental.

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Area of Science:

  • Nonlinear Dynamics
  • Information Theory
  • Complex Systems

Background:

  • Synchronization is a common phenomenon in coupled dynamical systems.
  • While often beneficial, synchronization can be harmful in certain real-world applications.
  • Early detection of harmful synchronization is therefore a critical requirement.

Purpose of the Study:

  • To propose a reliable measure (R) for the early detection of complete and generalized synchronization.
  • To utilize information theory concepts, specifically joint entropy and mutual information, for synchronization detection.

Main Methods:

  • Developed a novel measure (R) based on joint entropy and mutual information.
  • Validated the measure using numerical simulations of mathematical models.
  • Tested the measure with experimental data from turbulent thermoacoustic systems.

Main Results:

  • The proposed measure (R) effectively anticipates both complete and generalized synchronizations.
  • Demonstrated applicability across various coupled oscillator models, including chaotic systems.
  • Confirmed the measure's efficacy with real-world experimental data.

Conclusions:

  • The information-theoretic measure (R) provides a reliable method for early warning of harmful synchronization.
  • This approach is applicable to diverse coupled dynamical systems, from mathematical models to experimental setups.
  • Offers a valuable tool for mitigating risks associated with unwanted synchronization.