Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/27413
Title: Spectral criterion of stochastic stability for invariant manifolds 1
Authors: Ryashko, L. B.
Bashkirtseva, I. A.
Issue Date: 2013
Citation: Ryashko L. B. Spectral criterion of stochastic stability for invariant manifolds 1 / L. B. Ryashko, I. A. Bashkirtseva // Cybernetics and Systems Analysis. — 2013. — Vol. 49. — № 1. — P. 69-76.
Abstract: The mean square stability for invariant manifolds of nonlinear stochastic differential equations is considered. The stochastic stability analysis is reduced to the estimation of the spectral radius of some positive operator. For the important case of manifolds with codimension one, a constructive spectral analysis of this operator is carried out. On the basis of this spectral technique, parametrical criteria of the stochastic stability of limit cycle and 2-torus are developed. © 2013 Springer Science+Business Media New York.
Keywords: INVARIANT MANIFOLDS
SPECTRAL CRITERION
STOCHASTIC STABILITY
CODIMENSION
INVARIANT MANIFOLDS
LIMIT CYCLE
MEAN SQUARE STABILITY
POSITIVE OPERATOR
SPECTRAL CRITERIA
SPECTRAL RADII
SPECTRAL TECHNIQUES
STOCHASTIC DIFFERENTIAL EQUATIONS
STOCHASTIC STABILITY
SPECTRUM ANALYSIS
STOCHASTIC SYSTEMS
STABILITY CRITERIA
URI: http://hdl.handle.net/10995/27413
DOI: 10.1007/s10559-013-9486-3
SCOPUS: http://www.scopus.com/inward/record.url?eid=2-s2.0-84873708404&partnerID=40&md5=2369b3d9068cbd5c19ac6df7445020bc
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