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Synchronization transition in the Kuramoto model with colored noise
1Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We analyzed the stability of phase oscillators with colored noise, bridging a gap between white noise and quenched frequency cases. This provides new insights into complex system dynamics.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Globally coupled phase oscillators are fundamental models in various scientific fields.
- Previous analyses often simplified noise to white noise or quenched frequencies, limiting applicability.
- Understanding stability under more realistic colored noise is crucial.
Purpose of the Study:
- To perform a linear stability analysis of the incoherent state in globally coupled phase oscillators.
- To investigate the effects of colored noise on system stability.
- To bridge the analytical gap between white noise and quenched random frequency cases.
Main Methods:
- Linear stability analysis was employed.
- The system considered consists of identical phase oscillators with global coupling.
- Colored noise was introduced as a perturbation.
Main Results:
- The analysis successfully characterized the stability of the incoherent state under colored noise.
- A connection was established between the analytically solvable limits of white noise and quenched frequencies.
- The study provides a more comprehensive understanding of oscillator dynamics with realistic noise.
Conclusions:
- Linear stability analysis is effective for studying oscillator networks with colored noise.
- The findings extend the analytical tractability of coupled oscillator systems.
- This work offers a more nuanced perspective on synchronization and stability in complex systems.
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