Identifying the net information flow direction in mutually coupled non-identical chaotic oscillators

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.