Optimal phase synchronization in networks of phase-coherent chaotic oscillators

Area of Science:

• Complex Systems
• Network Science
• Nonlinear Dynamics

Background:

• Phase synchronization is crucial in many complex systems.
• Chaotic oscillators often exhibit complex behaviors.
• Network topology significantly influences system dynamics.

Purpose of the Study:

• To identify conditions for optimal phase synchronization in chaotic oscillators.
• To establish a link between oscillator frequencies and network topology.
• To minimize coupling strength for effective synchronization.

Main Methods:

• Definition of a synchrony alignment function J(ω,L).
• Numerical simulations using the Rössler system.
• Experimental validation with nonlinear electronic circuits.

Main Results:

• A synchrony alignment function J(ω,L) was defined, linking natural frequencies (ω) and network Laplacian (L).
• The function successfully predicts optimal phase synchronization conditions for chaotic oscillators.
• Experimental results confirm theoretical predictions, showing robustness against noise and parameter mismatch.

Conclusions:

• An optimal interplay between natural frequencies and network topology facilitates effective phase synchronization.
• The synchrony alignment function provides a powerful tool for designing and understanding synchronized chaotic systems.
• The findings are robust and applicable to real-world systems with inherent imperfections.