Adaptive Frequency Model for Phase-Frequency Synchronization in Large Populations of Globally Coupled Nonlinear Oscillators

Abstract

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.