Synchronized states in a ring of dissipatively coupled harmonic oscillators
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View abstract on PubMed
Summary
This summary is machine-generated.Researchers found that adjusting gain and loss in coupled harmonic oscillators can achieve stable synchronization. A scaling law, σ_{full}∼N^{-3/2}, was derived for synchronization under frequency fluctuations in larger systems.
Area Of Science
- Physics
- Nonlinear Dynamics
- Complex Systems
Background
- Synchronization of coupled oscillators is a fundamental phenomenon in various scientific disciplines.
- Understanding the conditions for stable synchronization in systems with frequency differences and dissipation is crucial.
Purpose Of The Study
- To investigate the conditions for achieving stable synchronized dynamics in a ring of harmonic oscillators with nearest-neighbor coupling.
- To analyze the impact of frequency fluctuations and system size on oscillator synchronization.
Main Methods
- Modeling a system of coupled harmonic oscillators with bilinear, dissipative nearest-neighbor coupling.
- Utilizing complex eigenvalues and eigenvectors of the non-Hermitian matrix to interpret system dynamics.
- Deriving a scaling law for synchronization under Gaussian frequency fluctuations.
Main Results
- Stable synchronized dynamics can be achieved by tuning gain and loss parameters.
- A complete analysis was performed for two oscillators and small ring sizes (N=5).
- A scaling law σ_{full}∼N^{-3/2} was derived for the maximum frequency fluctuation standard deviation (σ_{full}) allowing full synchronization for N≳10 oscillators with Gaussian fluctuations.
Conclusions
- The study demonstrates that controlled gain and loss can induce synchronization in coupled oscillators.
- Frequency fluctuations significantly influence synchronization timescales, affecting both the onset and decay of synchronized states.
- The derived scaling law provides a quantitative prediction for synchronization limits in larger, fluctuating oscillator networks.
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