External periodic driving of large systems of globally coupled phase oscillators.

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.