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Local synchronization in complex networks of coupled oscillators.
John Stout1, Matthew Whiteway, Edward Ott
1Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA. jestout@ncsu.edu
Chaos (Woodbury, N.Y.)
|July 5, 2011
Summary
Global synchronization in Kuramoto networks is robust to more oscillators or varied frequencies. However, increased network links per oscillator diminish this synchronization pathway, impacting cluster formation and merging.
Area of Science:
- Complex Systems
- Network Science
- Nonlinear Dynamics
Background:
- The Kuramoto model is a fundamental framework for studying synchronization phenomena in coupled oscillator systems.
- Previous research identified a specific synchronization pathway involving cluster formation, growth, and merging in these networks.
- Understanding factors influencing this pathway is crucial for predicting emergent collective behavior in complex systems.
Purpose of the Study:
- To investigate how network topology, natural frequency distribution, and system size affect global synchronization in Kuramoto networks.
- To analyze the robustness of the cluster-merging synchronization scenario under varying network parameters.
- To determine the impact of increasing coupling strength on the emergence of a macroscopic synchronized component.
Main Methods:
- Simulations of the Kuramoto model with varying network topologies, natural frequency distributions, and system sizes.
- Analysis of the synchronization process as coupling strength is systematically increased.
- Characterization of the formation, growth, and merging of synchronized clusters.
Main Results:
- The cluster-merging synchronization scenario is robust to increases in the number of oscillators.
- Variations in the distribution function of natural frequencies do not significantly disrupt this synchronization pathway.
- An increase in the number of links per oscillator leads to a less prominent emergence of the giant synchronized component.
Conclusions:
- The identified pathway to global synchronization in Kuramoto networks is generally stable across different system sizes and frequency distributions.
- Network connectivity, specifically the density of links, plays a critical role in modulating the prominence of this synchronization mechanism.
- These findings offer insights into the conditions governing emergent synchronized behavior in diverse complex systems.
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