Phase diagram of the random frequency oscillator: The case of Ornstein-Uhlenbeck noise

Details Phase diagram of the random frequency oscillator: The case of Ornstein-Uhlenbeck noise Phase diagram of the random frequency oscillator: The case of Ornstein-Uhlenbeck noise

2006-08-02

arxiv.org/abs/cond-mat/0608049v1

Physics

Condensed Matter

Statistical Mechanics

to appear in Physica D

Scientific paper

10.1016/j.physd.2006.07.013

We study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an Ornstein-Uhlenbeck noise. This system undergoes a noise-induced bifurcation when the amplitude of the noise grows. The critical curve, that separates the absorbing phase from an extended non-equilibrium steady state, corresponds to the vanishing of the Lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy. We derive various expressions for this Lyapunov exponent by using different approximation schemes. This allows us to determine quantitatively the phase diagram of the random parametric oscillator.

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