Abstract
A problem of the analysis of nonlinear dynamic systems forced by the random disturbances is considered. For the description of probabilistic distributions around the deterministic attractors, a theory of the quasipotential and its approximations based on the stochastic sensitivity functions (SSF) technique is suggested. Constructive methods for the computation of SSF for the equilibria and limit cycles are presented and discussed. We show how SSF can be used for the visual description of probabilistic distributions in the form of confidence domains.
Highlights
Currently, the stochastic dynamic systems are widely used for the modeling of processes in various fields of science [1]
For the analysis of nonlinear stochastic systems, we set forth a new constructive approach based on the stochastic sensitivity functions and confidence domains
If a character of the transient is unessential and the main interest is focused on the stable stationary regime, it is possible to restrict a stochastic analysis by the study of the stationary density function ρ(x, ε)
Summary
The stochastic dynamic systems are widely used for the modeling of processes in various fields of science [1]. As a result of stochastic forcing, the random trajectories of system (1) form some flow with the probability density function ρ(t, x, ε) This function is governed by the Kolmogorov-FokkerPlanck equation [4]. If a character of the transient is unessential and the main interest is focused on the stable stationary regime, it is possible to restrict a stochastic analysis by the study of the stationary density function ρ(x, ε). This function is a solution of the stationary KolmogorovFokker-Planck equation. We will present constructive methods of such approximations for equilibria and cycles
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