Transitions in a Duffing oscillator excited by random noise |
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Authors: | R. V. Bobryk A. Chrzeszczyk |
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Affiliation: | (1) Institute of Mathematics, Swietokrzyska Academy, 25-406 Kielce, Poland;(2) Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences, 79-060 Lviv, Ukraine |
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Abstract: | We investigate a Duffing oscillator driven by random noise which is assumed to be a harmonic function of the Wiener process. We show that the correlation time of the noise has a strong effect on the form of the response stationary probability density functions. It represents the so-called reentrance transitions, i.e. for the same noise intensity the probability density function has an identical modality for both the small and the large correlation time but a different modality for the moderate correlation time. The transitions are observed for both the single-well and twin-well potential case. A new approach is used to study the response probability density function. It is based on analysis of hyperbolic systems. |
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Keywords: | Duffing oscillator Noise-induced transition Probability density function Non-white noise excitation Hyperbolic system |
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