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Multiscale dynamics in communities of phase oscillators
Dustin Anderson1, Ari Tenzer, Gilad Barlev
1Department of Physics and Astronomy, Carleton College, Northfield, Minnesota 55057, USA.
Chaos (Woodbury, N.Y.)
|April 3, 2012
Summary
We studied coupled phase oscillators in groups with attractive and repulsive interactions. A new method reveals stable dynamics, showing how groups synchronize or repel based on system parameters.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Investigating synchronization in coupled oscillator systems is crucial for understanding emergent behavior in various fields.
- Heterogeneous frequencies and group structures introduce complexity to synchronization dynamics.
Purpose of the Study:
- To analyze the dynamics of many coupled phase oscillators organized into M groups.
- To explore synchronization and repulsion phenomena within and between these groups.
- To develop a reduced-order model for complex oscillator network dynamics.
Main Methods:
- Utilized the Ott-Antonsen ansatz to reduce the dimensionality of the governing equations.
- Analyzed the symmetric case to identify stable and unstable equilibria.
- Employed slow/fast timescale analysis for the asymmetric case to derive evolution equations.
Main Results:
- Identified a manifold (L) of neutrally stable equilibria in the symmetric case.
- Determined the dimension of the equilibrium manifold L (M-2 for M>=3, 1 for M=2).
- Derived slow time evolution equations for group dynamics in the asymmetric case, validated by simulations.
Conclusions:
- The Ott-Antonsen ansatz provides an effective reduction for analyzing complex coupled oscillator systems.
- The identified manifold of equilibria offers insights into the stable states of synchronized and repelling groups.
- The developed slow time evolution equations accurately capture the dynamics of asymmetric oscillator networks.
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