Self-consistent autocorrelation of a disordered Kuramoto model in the asynchronous state

Area of Science:

• Physics
• Complex Systems
• Nonlinear Dynamics

Background:

• The Kuramoto model is a key framework for understanding synchronization in coupled oscillators.
• The asynchronous regime within the Kuramoto model has been less explored.
• Understanding asynchronous dynamics is crucial for real-world coupled systems.

Purpose of the Study:

• To investigate the asynchronous state of the Kuramoto model with finite oscillators and disordered connectivity.
• To adapt and enhance the Stiller and Radons mean-field approach.
• To analyze power spectra and network noise in the asynchronous regime.

Main Methods:

• Utilized an iterative stochastic mean-field approximation.
• Reduced the N-oscillator system to one-dimensional dynamics.
• Applied the method to both homogeneous and heterogeneous networks.

Main Results:

• Successfully analyzed the asynchronous state in the Kuramoto model.
• Investigated power spectra of individual oscillators.
• Characterized the multiplicative network noise.

Conclusions:

• The enhanced mean-field approach effectively models asynchronous dynamics in finite, disordered Kuramoto systems.
• Findings are applicable to coupled oscillator systems in biology and technology.
• Provides a method to study previously neglected asynchronous regimes.