ИСТИНА

Strange and hyperbolic attractors. Strange (chaotic) attractors which are seen in the models of real physical systems possess some degree of hyperbolicity, however, this hyperbolicity has a form different from that of uniform hyperbolicity. Such attractors are, in fact, complicatedly organized sets, but they belong to a quasi - stochastic type ( i. e. they are quasi - attractors). Hyperbolic sets were consttructed rather long ago and, for a long time it was thought that the systems with such a structure of phase space were abstract mathematic constructions. However, recently were suggested physical models having attracting subsets possessing the properties of hyperbolicity. As it is known, for the resent 30 years one of the mostly demanded fields of inquiry in the theory of complex and chaotic systems has been the solution of the problem of controlling chaotic dynamics and chaos suppression by minor external influences. The investigation of recent years showed that the problem can be solved for a particular class of dynamic systems, however, the question about the systems with hyperbolic attractors remains open. It is connected with the fact that such attractors are rough and their structure can not change qualitatively with minor external influences. In the present contribution consideration is being given to an autonomous physical system which is characterized by the presence of the attractor of a hyperbolic type. We study the possibility of controlling and stabilizing the dynamics of the systems of this type by the Pyragas method.