SENSITIVITY ANALYSIS OF STOCHASTICALLY FORCED QUASIPERIODIC SELF-OSCILLATIONS / Bashkirtseva Irina,Ryashko Lev // ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - 2016. - V. , l. .

ISSN/EISSN:

1072-6691 / нет данных

Type:

Article

Abstract:

We study a problem of stochastically forced quasi-periodic 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 two-torus in the three-dimensional space, a constructive solution of this problem is given. Our theoretical results are illustrated with an example.

Author keywords:

Stochastic differential equations; tori; stochastic sensitivity; quasipotential HAMILTON-JACOBI EQUATIONS; SYSTEMS; HOMOGENIZATION; STABILITY; NOISE

DOI:

нет данных

Web of Science ID:

ISI:000382919400003

Соавторы в МНС:

Другие поля

Поле	Значение
Month	AUG 31
Publisher	TEXAS STATE UNIV
Address	601 UNIVERSTITY DRIVE, SAN MARCOS, TX 78666 USA
Language	English
Article-Number	240
Keywords-Plus	HAMILTON-JACOBI EQUATIONS; SYSTEMS; HOMOGENIZATION; STABILITY; NOISE
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	irina.bashkirtseva@urfu.ru lev.ryashko@urfu.ru
Funding-Acknowledgement	Russian Science Foundation {[}N 16-11-10098]
Funding-Text	The work was supported by Russian Science Foundation (N 16-11-10098)
Number-of-Cited-References	36
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	1
Journal-ISO	Electron. J. Differ. Equ.
Doc-Delivery-Number	DV4TZ