Approximate analytic solutions for noise-induced coherent oscillations in autonomous nonlinear systems

Abstract

Noise-induced coherent oscillations in autonomous nonlinear systems, recently found in numerical studies by Gang et al. [Phys. Rev. Lett. 71, 807 (1993)], are explained in simple terms by obtaining approximate analytical solutions in the weak-noise regime. The creation by noise of asymptotic collective oscillations in deterministic systems near saddle-node bifurcation points is understood as a process of generation of probability currents in effective monodimensional potentials. The knowledge of the functional dependence of the mean frequency on the parameters of the system gives insight into the mechanisms responsible for specific features of these resonancelike responses to noise.