Stochastic Kuramoto oscillators with discrete phase states

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• The Kuramoto model is a foundational framework for studying synchronization in coupled oscillators.
• Understanding the impact of stochasticity and discrete dynamics on oscillator networks is crucial.

Purpose of the Study:

• To generalize the Kuramoto model by incorporating discrete phase increments and stochastic processes.
• To investigate the effects of phase discretization on synchronization and oscillation precision.

Main Methods:

• Analytical investigation of the phase-discretized oscillator model.
• Numerical simulations to explore system dynamics and properties.
• Utilizing a Markov chain framework to model coupled oscillations.

Main Results:

• Phase discretization introduces distinct extrema in key observables like steady-state synchrony.
• The model exhibits unique synchronization and precision behaviors not present in the continuous Kuramoto model.
• Convergence to the classical Kuramoto model is observed in the continuous phase limit.

Conclusions:

• The phase-discretized Kuramoto model offers a more general framework for stochastic coupled oscillations.
• Discrete phase dynamics significantly influence network synchronization and oscillation quality.
• This model provides a novel perspective on coupled oscillator systems within a Markov chain setting.