Long-term fluctuations in globally coupled phase oscillators with general coupling: finite size effects

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• The Kuramoto model describes synchronization in coupled oscillators.
• Understanding fluctuations in macroscopic system behavior is crucial.
• Existing models like the Ising model show consistent scaling properties.

Purpose of the Study:

• Investigate the diffusion coefficient of the time integral of the Kuramoto order parameter.
• Characterize long-term fluctuations in globally coupled nonidentical phase oscillators.
• Analyze the scaling law of a derived quantity D (N times the diffusion coefficient) with system size N.

Main Methods:

• Introduce a statistical quantity D = N * diffusion coefficient.
• Analyze the scaling behavior of D with system size N.
• Compare scaling laws across different coupling schemes and regimes (coherent vs. incoherent).

Main Results:

• The scaling law of D differs between coherent and incoherent regimes for phase oscillators.
• In the coherent regime, D scales as O(1/N^a) with a > 0.
• In the incoherent regime, D scales as O(1), similar to the Ising model.

Conclusions:

• The scaling properties of fluctuations in globally coupled phase oscillators are distinct from models like the Ising model.
• The observed scaling laws are robust across various coupling schemes.
• This finding provides new insights into the collective dynamics and fluctuation characteristics of oscillator networks.