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Persistent fluctuations in synchronization rate in globally coupled oscillators with periodic external forcing
1Department of Physics, Kyoto University, Japan. atsumi@scphys.kyoto-u.ac.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
Synchronization rate fluctuations in phase oscillator systems persist and scale with system size for random initial conditions. These fluctuations arise from collective dynamics, influenced by initial phase distribution inhomogeneity.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Phase oscillator systems with global coupling are fundamental models in physics.
- Understanding synchronization dynamics and fluctuations is crucial for complex systems research.
- Periodic forcing and repulsive coupling introduce rich dynamical behaviors.
Purpose of the Study:
- To investigate the nature and origin of persistent fluctuations in the synchronization rate of a forced phase oscillator system.
- To analyze the relationship between system size, initial phase distribution, and fluctuation amplitude.
- To elucidate the underlying dynamics responsible for synchronization rate variations.
Main Methods:
- Analysis of a system of phase oscillators with repulsive global coupling and periodic external forcing.
- Application of the Watanabe-Strogatz transformation to derive low-dimensional macroscopic equations.
- Investigation of system-size scaling for uniformly random initial phase distributions.
Main Results:
- Synchronization rate exhibits persistent fluctuations dependent on parameters and initial conditions.
- Fluctuation amplitude scales with system size for uniformly random initial phases.
- Fluctuations correspond to collective dynamics and low-dimensional trajectories of the reduced system.
Conclusions:
- The observed fluctuations are collective phenomena of the oscillator system.
- Initial phase distribution inhomogeneity is a key determinant of fluctuation amplitude.
- The Watanabe-Strogatz transformation provides a powerful tool for analyzing such complex dynamics.
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