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.
Keywords: invariant manifolds, stochastic stability, spectral criterion.
Ряшко Лев Борисович,
доктор физ.-мат. наук, профессор Уральского федерального университета, Екатеринбург, Россия,
e-mail: lev.ryashko@usu.ru.
Башкирцева Ирина Адольфовна,
кандидат физ.-мат. наук, доцент Уральского федерального университета, Екатеринбург, Россия,
e-mail: irina.bashkirtseva@usu.ru.