Coherence resonance at noisy precursors of bifurcations in nonlinear dynamical systems

Abstract

A general mechanism of coherence resonance that occurs in noisy dynamical systems close to the onset of bifurcation is demonstrated through examples of period-doubling and torus-birth bifurcations. Near the bifurcation of a periodic orbit, noise produces the characteristic peaks of ``noisy precursors'' in the power spectrum. The signal-to-noise ratio evaluated at these peaks is maximal for a certain optimal noise intensity in a manner that resembles a stochastic resonance.