Article ID Journal Published Year Pages File Type
1898241 Physica D: Nonlinear Phenomena 2006 12 Pages PDF
Abstract

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 study quantitatively the phase diagram of the random parametric oscillator.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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