Synchronization of driven nonlinear oscillators

Mathematical models of nonlinear oscillators are used to describe a wide variety of physical and biological phenomena that exhibit self-sustained oscillatory behavior. When these oscillators are strongly driven by forces that are periodic in time, they often exhibit a remarkable “mode-locking” that synchronizes the nonlinear oscillations to the driving force. The purpose of this paper is to demonstrate that a similar phenomenon occurs when nonlinear oscillators are strongly driven by a force that is varying randomly in time. In this case the synchronization is less obvious for a single oscillator, but when several oscillators with different initial conditions or phases are driven with the same aperiodic force, their fluctuating behavior may reliably converge to an identical response. Analytical estimates are derived for the conditions, rates, and structural stability for the synchronization of a broad class of aperiodically driven nonlinear oscillators.