Spectral Criterion of Stochastic Stability for Invariant Manifolds
نویسندگان
چکیده
SPECTRAL CRITERION OF STOCHASTIC STABILITY FOR INVARIANT MANIFOLDS 1 L. B. Ryashko a† and I. A. Bashkirtseva a‡ UDC 531.36 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.
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