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Large systems of coupled oscillators subjected to a periodic external driveoccur in many situations in physics and biology. Here the simple, paradigmaticcase of equal-strength, all-to-all sine-coupling of phase oscillators subjectto a sinusoidal external drive is considered. The stationary states and theirstability are determined. Using the stability information and numericalexperiments, parameter space phase diagrams showing when different types ofsystem behavior apply are constructed, and the bifurcations marking transitionsbetween different types of behavior are delineated. The analysis is supportedby results of direct numerical simulation of an ensemble of oscillators.

External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators