Bifurcations in the Kuramoto model with external forcing and higher-order interactions

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here we investigate this model in the presence of two characteristics that may be important in applications: an external periodic influence and higher-order interactions among the units. The combination of these ingredients leads to a very rich bifurcation scenario in the dynamics of the order parameter that describes phase transitions. Our theoretical calculations are validated by numerical simulations.