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Inferring the connectivity of coupled chaotic oscillators using Kalman filtering.

E Forero-Ortiz1, G Tirabassi1, C Masoller1

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This study introduces the Kalman filter (KF) for inferring interactions in coupled chaotic oscillators. The KF successfully reconstructs network topology and coupling strength using minimal data, even near synchronization.

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Area of Science:

  • Complexity science
  • Nonlinear dynamics
  • Network science

Background:

  • Inferring interactions in coupled oscillators is crucial for understanding complex systems.
  • The Kalman filter (KF) is established for data assimilation but not applied to inferring chaotic oscillator connectivity.
  • Coupled chaotic oscillators exhibit complex dynamics with broad interdisciplinary relevance.

Purpose of the Study:

  • To demonstrate the applicability of the Kalman filter (KF) for inferring the interaction topology and coupling strength of chaotic oscillators.
  • To show that KF can reconstruct network properties using limited observational data.
  • To validate the method's effectiveness even in near-synchronization regimes.

Main Methods:

  • Utilized the Kalman filter (KF) technique to analyze the dynamics of coupled Rössler-like chaotic oscillators.
  • Reconstructed interaction topology and coupling strength by observing a single variable from each oscillator's phase space.
  • Simulated network behavior under varying coupling strengths and proximity to synchronization.

Main Results:

  • Successfully inferred the interaction topology and coupling strength of a network of chaotic oscillators using KF.
  • Demonstrated that connectivity can be determined from a single observed variable per oscillator.
  • Showed that network properties are accurately retrievable even when oscillators are near synchronization.

Conclusions:

  • The Kalman filter (KF) provides an effective method for inferring the connectivity of coupled chaotic oscillators.
  • The proposed KF-based approach is robust, requiring minimal observational data.
  • This method advances the analysis of complex networks in nonlinear dynamics and related fields.