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We study the dynamics of a classical nonlinear oscillator subject to noiseand driven by a sinusoidal force. In particular, we give an analyticalidentification of the mechanisms responsible for the supernarrow peaks observedrecently in the spectrum of a mechanical realization of the system. Ourapproach, based on the application of averaging techniques, simulates standarddetection schemes used in practice. The spectral peaks, detected in a range ofparameters corresponding to the existence of two attractors in thedeterministic system, are traced to characteristics already present in thelinearized stochastic equations. It is found that, for specific variations ofthe parameters, the characteristic frequencies near the attractors converge onthe driving frequency, and, as a consequence, the widths of the peaks in thespectrum are significantly reduced. The implications of the study to thecontrol of the observed coherent response of the system are discussed.

Coherent response of a stochastic nonlinear oscillator to a driving force: analytical characterization of the spectral signatures