Moscow State University
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. Thus, we have shown that external periodic perturbations can crucially effect on the behaviour of the quadratic map family, a piecewise linear map family and the map with the hyperbolic attractor. Moreover, for maps having critical points the chosen in advance periodic orbits can be extracted and stabilized.On the basis of the Melnikov method we analytically considered the effect of perturbations on a two- dimensional non-autonomous system. In general, we have got an explicit analytical form of the external stabilized perturbations which allows us to suppress chaos. By this reason the obtained results can be applied to the systems and models of various nature for which the separatrix splitting phenomenon is inherent.