Synchronization and resonance in a driven system of coupled oscillators

Area of Science:

• Physics
• Nonlinear Dynamics
• Complex Systems

Background:

• Globally coupled oscillators are fundamental models in physics and neuroscience.
• Understanding noise effects is crucial for real-world systems exhibiting collective behavior.

Purpose of the Study:

• To investigate the influence of noise on driven globally coupled oscillators.
• To analyze the interplay between external driving and noise in synchronization dynamics.

Main Methods:

• Derivation of the self-consistency equation for the order parameter.
• Analysis of the order parameter's total and periodic components.
• Examination of the phase velocity response to varying noise levels.

Main Results:

• The total order parameter decreases monotonically with increasing noise, indicating overall synchronization suppression.
• For strong coupling, an optimal noise level maximizes the periodic component of the order parameter.
• Phase velocity exhibits resonance behavior, demonstrating complex responses to noise.

Conclusions:

• Noise generally suppresses synchronization in driven coupled oscillators.
• A nuanced relationship exists where specific noise levels can enhance collective periodic behavior.
• The system displays resonance phenomena in response to noise, highlighting complex dynamics.