A Closure Method for Randomly Perturbed Linear Systems

Bobryk, Roman V.; Stettener, Ł.

doi:10.1515/dema-2001-0219

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Response Probability Density Functions1

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2007

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“…Similar hierarchies were obtained for other dynamical systems in [28][29][30]. Of course we have to close this hierarchy to evaluate p(t, x, y).…”

Section: Response Probability Density Functionssupporting

confidence: 62%

Transitions in a Duffing oscillator excited by random noise

Bobryk

Chrzeszczyk

2007

Nonlinear Dyn

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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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“…Similar hierarchies were obtained for other dynamical systems in [28][29][30]. Of course we have to close this hierarchy to evaluate p(t, x, y).…”

Section: Response Probability Density Functionssupporting

confidence: 62%