Electron. J. Differential Equations,
Vol. 2016 (2016), No. 240, pp. 112.
Sensitivity analysis of stochastically forced quasiperiodic
selfoscillations
Irina Bashkirtseva, Lev Ryashko
Abstract:
We study a problem of stochastically forced quasiperiodic
selfoscillations 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 twotorus in the threedimensional space, a constructive
solution of this problem is given. Our theoretical results are illustrated
with an example.
Submitted May 30, 2016. Published August 31, 2016.
Math Subject Classifications: 34D35, 37H10, 34K14.
Key Words: Stochastic differential equations; tori; stochastic sensitivity;
quasipotential.
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Irina Bashkirtseva
Ural Federal University
Pr. Lenina 51, Ekaterinburg 620083, Russia
email: irina.bashkirtseva@urfu.ru


Lev Ryashko
Ural Federal University
Pr. Lenina 51, Ekaterinburg 620083, Russia
email: lev.ryashko@urfu.ru

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