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Delays induced cluster synchronization in chaotic networks.

Chad Nathe¹, Ke Huang¹, Matteo Lodi²

¹Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA.

Chaos (Woodbury, N.Y.)

|December 31, 2020

Summary

Coupling delays in networks of coupled oscillators significantly influence cluster synchronization patterns. Researchers found that specific delay arrangements can stabilize various synchronization patterns in experimental and theoretical models.

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Area of Science:

Complex Systems
Nonlinear Dynamics
Network Science

Background:

Synchronization is a fundamental phenomenon in coupled oscillator networks.
Coupling delays can drastically alter network dynamics and emergent behaviors.
Understanding delay effects is crucial for designing and controlling complex systems.

Purpose of the Study:

To investigate the impact of coupling delays on cluster synchronization patterns.
To analyze the stability of different cluster synchronization patterns.
To validate theoretical predictions with experimental observations.

Main Methods:

Theoretical analysis of coupled identical oscillators in a ring network.
Stability analysis of emergent cluster synchronization patterns.
Experimental realization using Colpitts oscillators with RF cable delays.
Verification on a larger, fully connected network with probabilistic delays.

Main Results:

Eight distinct cluster synchronization patterns emerge in a six-oscillator ring network based on delay assignments.
All identified patterns can be stabilized for sufficient coupling strength and specific delay values.
Experimental results closely match theoretical predictions for cluster synchronization.
Theory validated on a 50-node network with random delay distribution.

Conclusions:

Coupling delays are critical determinants of cluster synchronization in oscillator networks.
The precise arrangement of delays dictates emergent synchronization patterns.
Experimental validation confirms the theoretical framework for delay-coupled oscillator networks.