Time shifts and correlations in synchronized chaos

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Coupled dynamical systems often exhibit synchronized behavior.
• Unidirectional coupling schemes are prevalent in various scientific and engineering fields.
• Predicting and controlling synchronization properties remains a key challenge.

Purpose of the Study:

• To introduce a novel transfer function-based method for predicting synchronization characteristics.
• To quantify the correlation and time shift in unidirectional coupling schemes.
• To enable the design of improved coupling strategies for enhanced synchronization.

Main Methods:

• Derivation of a transfer function from the coupling model.
• Application of the transfer function to simulated coupled Rossler oscillators.
• Validation using an experimental system of coupled chaotic electronic circuits.

Main Results:

• The transfer function accurately estimates correlation between drive and response waveforms.
• The method provides reliable predictions of the time shift (lag or anticipation) in synchronized states.
• Demonstrated significant improvements in correlation and maximum achievable time shift using designed coupling schemes.

Conclusions:

• The developed transfer function offers a powerful tool for analyzing and predicting synchronization in unidirectional coupled systems.
• This method facilitates the design of novel coupling schemes with enhanced performance.
• The findings have implications for controlling and optimizing synchronized behavior in complex networks.