Adaptive frequency model for phase-frequency synchronization in large populations of globally coupled nonlinear oscillators

Phase models describing self-synchronization phenomena in populations of globally coupled oscillators are generalized including "inertial" effects. This entails that the oscillator frequencies also vary in time along with their phases. The model can be described by a large set of Langevin equations when noise effects are also included. Also, a description of such systems can be given in the thermodynamic limit of infinitely many oscillators via a suitable Fokker-Planck-type equation. Numerical simulations confirm that simultaneous synchronization of phases and frequencies is possible when the coupling strength goes to infinity.