Mechanisms of non-feedback controlling chaos and suppression of chaotic motion

We describe a rigorous approach to the investigation of qualitative changes in the behaviour of chaotic dynamical systems under external periodic perturbations and propose an analytical key to find such perturbations. It is proven that through a simple periodic perturbation one can stabilize the chosen periodic orbits of any unimodal maps. As an example the quadratic family maps is investigated. Also, it is proven that for piecewise linear family maps and for a two-dimensional map having a hyperbolic attractor there are feedback-free perturbations which lead to suppression of chaos and stabilization of certain periodic orbits.