A noisy damping parameter in the equation of motion of a
nonlinear oscillator renders the fixed point of the system
unstable when the amplitude of the noise is sufficiently large.
However, the stability diagram of the system can not be predicted
from the analysis of the moments of the linearized equation.
In the case of a white noise, an exact formula for
the Lyapunov exponent of the system is derived.
We then calculate the critical
damping for which the nonlinear system becomes unstable.
We also characterize the intermittent structure of the
bifurcated state above threshold and address the effect of
temporal correlations of the noise by considering an
02.50.-r Probability theory, stochastic processes and
statistics (see also section 05
Statistical physics, thermodynamics,
and nonlinear dynamical systems) 05.40.-a Fluctuation phenomena, random process,
noise and Brownian motion 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
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