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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2005

Nonlinear oscillator with parametric colored noise: some analytical results

Résumé

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit.
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Dates et versions

hal-00014740 , version 1 (21-04-2023)

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Kirone Mallick, Philippe Marcq. Nonlinear oscillator with parametric colored noise: some analytical results. Journal of Physics A: Mathematical and Theoretical, 2005, 38, pp.5913-5927. ⟨10.1088/0305-4470/38/26/006⟩. ⟨hal-00014740⟩
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