THE ROLE OF NOISE ON THE SYNCHRONIZATION OF OSCILLATORS

Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. For long time, noise has been considered a nuisance for synchronization, but recent developments, e.g. stochastic resonance, reveals that noise can play an active role to enhance self organization. Traditionally, phase noise has been described as a diffusion process, i.e. noise is responsible for phase diffusion, leaving the oscillation frequency unchanged. We show that phase noise in oscillator is best described as a convection diffusion problem, i.e. noise is responsible for both phase diffusion and frequency drift. We derive a simplified model to study the influence if noise on the oscillation frequency, and we discuss the implication to the synchronization of coupled and periodically driven oscillators