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Stochastic jump phenomena in the random responses of a Duffing oscillator subjected to nonwhite random excitation are investigated. The stochastic jump phenomena correspond to the existence of multiple stationary responses, which differ in the phase angle between excitation and response as well as the amplitude of responses. The response suddenly switches to other stationary response in the long sample function. The purpose of this paper is to propose the criterion that is able to distinguish between two states of the response when the band width of the random excitation becomes broader. In this study, we propose the product of each wavelet transform of the excitation and the response to estimate the phase angle between them. Numerical examples show that the product corresponds to the frequency decomposed phase angle between the excitation and the response, and successfully identifies the states of the response.

Time Series Analysis for Jump Phenomena in Random Responses of a Duffing Oscillator Using Continuous Wavelet Transforms