Synchronization of randomly driven nonlinear oscillators

When nonlinear oscillators with stable limit cycles are subject to periodic forces, these oscillators may become entrained or mode locked to the driving force. Remarkably, a similar phenomenon occurs when the nonlinear oscillators are driven by a random force. In particular, when nonlinear oscillators with different initial conditions are strongly driven with the same random force, their fluctuating behavior may reliably converge to an identical, synchronized response. Analytical estimates are derived for the conditions, rates, and structural stability for synchronization of a broad class of randomly driven nonlinear oscillators, which suggest different experimental procedures for assessing the nonlinear response of biological, chemical, and physical oscillators to fluctuating inputs.