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Synchronization in large directed networks of coupled phase oscillators
Juan G Restrepo1, Edward Ott, Brian R Hunt
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA. juanga@math.umd.edu
Chaos (Woodbury, N.Y.)
|April 8, 2006
Summary
We study collective synchronization in complex networks using a generalized Kuramoto model. Our theory accurately predicts synchronization in directed networks with mixed coupling strengths.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- The Kuramoto model describes synchronization in coupled oscillators.
- Real-world networks often exhibit directed and heterogeneous coupling.
- Existing theories primarily focus on undirected networks.
Purpose of the Study:
- To generalize the Kuramoto model for directed networks.
- To extend synchronization theory to heterogeneous and directed systems.
- To analyze networks with mixed positive-negative coupling strengths.
Main Methods:
- Generalization of the classical Kuramoto model.
- Extension of theoretical approximations for synchronization transitions.
- Numerical simulations on directed networks.
Main Results:
- The developed theory accurately describes synchronization in directed networks.
- Good agreement was found between theoretical predictions and numerical simulations.
- The model accounts for network heterogeneity and mixed coupling.
Conclusions:
- The generalized Kuramoto model provides a robust framework for studying synchronization in complex directed networks.
- This work extends the understanding of collective dynamics in realistic network structures.
- The findings are applicable to various systems exhibiting synchronized behavior.
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