| Summary: | We study a problem of stochastically forced quasi-periodic
self-oscillations of nonlinear dynamic systems, which are modelled
by an invariant torus in the phase space.
For weak noise, an asymptotic of the stationary distribution of
random trajectories is studied using the quasipotential.
For the constructive analysis of a probabilistic distribution near
a torus, we use a quadratic approximation of the quasipotential.
A parametric description of this approximation is based on the stochastic
sensitivity functions (SSF) technique. Using this technique,
we create a new mathematical method for the probabilistic analysis
of stochastic flows near the torus. The construction of SSF is reduced
to a boundary value problem for a linear differential matrix equation.
For the case of the two-torus in the three-dimensional space, a constructive
solution of this problem is given. Our theoretical results are illustrated
with an example.
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