Stochastic sensitivity of the closed invariant curves for discrete-time systems

Discrete-time nonlinear systems with invariant closed smooth curves forced by random disturbances are studied. Constructive approximations of the corresponding probabilistic distributions near these curves based on stochastic sensitivity functions are suggested. For stochastic sensitivity matrix functions, the linear equations are obtained. For descriptive visualization of this technique, a method of confidence domains is used. The elaborated theory is illustrated on the example of the two-dimensional model.