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Extended finite-size scaling of synchronized coupled oscillators
Chulho Choi1, Meesoon Ha, Byungnam Kahng
1Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 16, 2013
Summary
We analyzed dynamic scaling in phase synchronization for coupled oscillators using the Kuramoto model. This study determines critical exponents and critical coupling strength for nonidentical frequencies.
Area of Science:
- Physics
- Complex Systems
- Nonlinear Dynamics
Background:
- Phase synchronization is crucial in coupled oscillator systems.
- Understanding dynamic scaling provides insights into system behavior near critical points.
Purpose of the Study:
- To systematically analyze dynamic scaling in the phase order parameter evolution.
- To extend finite-size scaling (FSS) from steady states to dynamic processes.
- To determine critical exponents and critical coupling strength for nonidentical coupled oscillators.
Main Methods:
- Systematic analysis of dynamic scaling in the Kuramoto model.
- Extension of finite-size scaling (FSS) theory to dynamic regimes.
- Numerical confirmation of theoretical predictions.
Main Results:
- Determined critical exponents and critical coupling strength.
- Demonstrated dynamic scaling allows measurement of FSS and thermodynamic critical exponents.
- Quantified the impact of frequency sampling and thermal noise on dynamic scaling.
Conclusions:
- Dynamic scaling offers a comprehensive approach to phase synchronization analysis.
- The extended FSS theory accurately describes dynamic scaling in finite systems.
- Frequency distribution and noise significantly influence dynamic scaling behavior.
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