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Area of Science:

  • Nonlinear Dynamics
  • Information Theory
  • Complex Systems

Background:

  • Coupled chaotic oscillators are fundamental in understanding complex systems.
  • Determining the direction of information flow in such systems is crucial but challenging.
  • Existing methods often rely on specific model assumptions.

Purpose of the Study:

  • To investigate the direction of net information flow between mutually coupled non-identical chaotic oscillators.
  • To establish a general principle governing information transfer based on the inherent chaoticity of individual oscillators.
  • To validate findings across diverse coupled oscillator configurations.

Main Methods:

  • Utilized conditional mutual information as a model-free, asymmetric index for information flow.
  • Defined the
  • degree of chaos
  • by the maximum Lyapunov exponent.
  • Calculated projected Kolmogorov-Sinai entropy for interacting oscillator variables.
  • Employed the Liang-Kleeman information flow measure for result validation.

Main Results:

  • A predominant net information transfer was observed from the oscillator with a higher degree of chaos to the one with a lower degree.
  • Oscillators with higher degrees of chaos exhibited higher projected Kolmogorov-Sinai entropy.
  • Results were consistent across oscillators with identical functional forms (different parameters) and entirely different functional forms.
  • The principle was also demonstrated in systems with oscillators of different phase space dimensions.

Conclusions:

  • The direction of net information flow in coupled non-identical chaotic oscillators is primarily dictated by their relative degrees of chaos.
  • The findings are robust and applicable to a wide range of coupled chaotic systems, irrespective of their specific dynamics or dimensions.
  • This provides a fundamental insight into information processing in complex chaotic networks.