Effect of adaptation functions and multilayer topology on synchronization

This study investigates the synchronization of globally coupled Kuramoto oscillators in monolayer and multilayer configurations. The interactions are taken to be pairwise, whose strength adapts with the instantaneous synchronization order parameter. The route to synchronization is analytically investigated using the Ott-Antonsen ansatz for two broad classes of adaptation functions that capture a wide range of transition scenarios. The formulation is subsequently extended to adaptively coupled multilayer configurations, using which a wider range of transition scenarios is uncovered for a bilayer model with cross-adaptive interlayer interactions.