Effects of parametric noise on a nonlinear oscillator

Details Effects of parametric noise on a nonlinear oscillator Effects of parametric noise on a nonlinear oscillator

2003-01-15

arxiv.org/abs/cond-mat/0301259v1

Physica A Vol. 325, pp. 213-219 (2003)

Physics

Condensed Matter

Statistical Mechanics

To be published in Physica A

Scientific paper

10.1016/S0378-4371(03)00200-0

We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow algebraically with time before the dissipative time scale is reached, and calculate the associated anomalous diffusion exponents. In the case of colored noise, with a nonzero but arbitrarily small correlation time, the characteristic exponents are modified. We determine their values thanks to a self-consistent Ansatz.

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