Parametric perturbations and non-feedback controlling chaotic motion

In this paper we generalize analytic studies the problems related to suppression of chaos and non-feedback controlling chaotic motion. We develop an analytic method of the investigation of qualitative changes in chaotic dynamical systems under certain external periodic perturbations. It is proven that for polymodal maps one can stabilize chosen in advance periodic orbits. As an example, the quadratic family of maps is considered. Also we demonstrate that for a piecewise linear family of maps and for a two-dimensional map having a hyperbolic attractor there are feedback-free perturbations which lead to the suppression of chaos and stabilization of certain periodic orbits.