Analysis of the stochastically forced invariant manifolds of dynamic systems

Abstract

We consider the randomly forced invariant manifolds of nonlinear dynamic systems. To study the dispersion of random states near the general deterministic attractors, we discuss two approaches. The first approach is based on the approximation of the quasipotential, and the second one uses the linear extension systems. A new semi-analytical method based on the stochastic sensitivity functions is suggested. The corresponding mathematical theory is shortly presented. Constructive applications of this theory to the analysis of equilibria and oscillatory regimes are given. © 2017 Author(s).