Evaluation of closure strategies for a periodically-forced Duffing oscillator with slowly modulated frequency subject to Gaussian white noise

• Four reduced stochastic models are compared to Monte Carlo simulations.
• A second-order cumulant neglect method for slowly ramped noisy frequency is proposed.
• The ratio of noise variance to chirp rate determines the response.

The response of a Duffing oscillator subject to a periodic forcing with slowly and stochastically modulated frequency is analyzed numerically. The results of both moment and cumulant-based stochastic reductions are compared to Monte Carlo simulations. It is shown how the explicit characterization of higher-order central moments of the (Gaussian) noise source and the periodic nature of the forcing enable a reliable reduction strategy providing a faithful description of the mean behavior of stochastic solutions. The reduced model is then used to illustrate how a large noise level and fast frequency drift may combine to sustain a strong response that is normally associated to resonance in the noiseless static case.