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Coupling in complex systems as information transfer across time scales.

Milan Paluš1

  • 1Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Prague 8, Praha, Czech Republic.

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This study introduces a method to detect cross-scale causal interactions in complex systems. It uses information theory and computational statistics to infer driver-response relationships from system dynamics.

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Area of Science:

  • Complex Systems Science
  • Nonlinear Dynamics
  • Information Theory
  • Computational Statistics

Background:

  • Complex systems (e.g., brain, climate) involve numerous interacting subsystems with nonlinear dynamics.
  • Variability spans multiple spatial and temporal scales, with inter-scale influences.
  • Detecting causal interactions across these scales is crucial for understanding system behavior.

Purpose of the Study:

  • To review and demonstrate a method for detecting cross-scale causal interactions in complex systems.
  • To infer driver-response relationships from the amplitudes and phases of coupled nonlinear dynamical systems.
  • To apply the methodology to analyze interactions within the El Niño Southern Oscillation.

Main Methods:

  • Combines information-theoretic formulation of Granger causality with computational statistics (surrogate data method).
  • Employs wavelet decomposition to separate multi-scale signals into quasi-oscillatory modes (phases and amplitudes).
  • Utilizes conditional mutual information to test causality between phases and amplitudes across different time scales.

Main Results:

  • Demonstrates the inference of driver-response relations from amplitudes and phases of coupled nonlinear dynamical systems.
  • Successfully applies the methodology to analyze cross-scale interactions and information transfer in the El Niño Southern Oscillation.
  • Provides a framework for understanding dynamical interaction mechanisms across scales in various scientific domains.

Conclusions:

  • The reviewed methodology effectively detects cross-scale causal interactions in complex systems.
  • Conditional mutual information applied to wavelet-decomposed signals is a powerful tool for causality inference.
  • Understanding these interactions is vital for modeling and predicting the behavior of systems like ENSO.