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Phase clustering in complex networks of delay-coupled oscillators
Toni Pérez1, Víctor M Eguíluz, Alex Arenas
1Physics Department, Lehigh University, Bethlehem, Pennsylvania 18015, USA. amp609@lehigh.edu
Chaos (Woodbury, N.Y.)
|July 5, 2011
Summary
We explore phase oscillator synchronization in complex networks with coupling delays. A new frequency adaptation rule and mean-field theory accurately predict synchronization in real-world systems.
Area of Science:
- Complex systems
- Network science
- Nonlinear dynamics
Background:
- Phase oscillators are fundamental units in many natural and engineered systems.
- Coupling delays and network topology significantly influence oscillator synchronization.
- Understanding clusterization and synchronization is crucial for system stability and function.
Purpose of the Study:
- To investigate the clusterization of phase oscillators with coupling delays in complex networks.
- To develop analytical tools for predicting synchronization phenomena.
- To propose methods for achieving perfect synchronization.
Main Methods:
- Formulation of equations for functional response in diffusive oscillators.
- Exact solutions for perfect synchronization in directed networks.
- Comparison of linear system solutions for nonlinear couplings.
- Development of a frequency adaptation rule.
- Proposal of a mean-field theory for random networks.
Main Results:
- Exact solutions for perfect synchronization in directed networks were obtained.
- A reliable method for predicting phase synchronization in real topologies was developed.
- The proposed frequency adaptation rule effectively achieves perfect synchronization.
- The mean-field theory accurately predicts phase synchronization in complex networks.
Conclusions:
- The study provides a robust framework for analyzing synchronization in complex networks.
- The developed methods and theories offer practical tools for controlling and predicting oscillator behavior.
- Findings are applicable to diverse systems, including biological networks and autonomous systems.
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