External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators

Abstract

Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, all-to-all sine-coupling of phase oscillators subject to a sinusoidal external drive is considered. The stationary states and their stability are determined. Using the stability information and numerical experiments, parameter space phase diagrams showing when different types of system behavior apply are constructed, and the bifurcations marking transitions between different types of behavior are delineated. The analysis is supported by results of direct numerical simulation of an ensemble of oscillators.

References in corpus (3)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• The Spectrum of the Partially Locked State for the Kuramoto Model
• Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing

Cited by in corpus (5)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Stability diagram for the forced Kuramoto model
• Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
• Echo Phenomena in Large Systems of Coupled Oscillators