Intermittent Bellerophon state in frequency-weighted Kuramoto model

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• The Bellerophon state, a quantized, time-dependent clustering phenomenon, was recently identified in globally coupled oscillators.
• Key characteristic: oscillators divide into clusters with differing instantaneous frequencies but synchronized average frequencies.

Purpose of the Study:

• To further characterize the intermittent Bellerophon state within the frequency-weighted Kuramoto model.
• To investigate the influence of a biased Lorentzian frequency distribution on this state's dynamics.

Main Methods:

• Utilized the frequency-weighted Kuramoto model, a standard framework for analyzing coupled oscillator systems.
• Employed a biased Lorentzian distribution for natural frequencies to simulate realistic oscillator populations.
• Analyzed the temporal evolution of oscillator states to identify intermittent dynamics.

Main Results:

• Identified an intermittent Bellerophon state characterized by periodic bursts of activity followed by longer resting periods.
• Observed a synchronous pattern in the bursting and resting phases across the oscillator population.
• Demonstrated that the intermittent Bellerophon state emerges under specific frequency distribution conditions.

Conclusions:

• The intermittent Bellerophon state represents a significant dynamical feature in coupled oscillator systems.
• The findings suggest that Bellerophon-like states may be a generic phenomenon in Kuramoto-like models.
• This research broadens the understanding of complex collective behaviors in diverse oscillatory networks.