Conditional attractors and regularization of chaotic systems

Spatial representation of many chaotic systems contains multidimensional geometric objects (conditional attractors) similar to ordinary nonlinear invariant and attracting sets. This observation points to the way to the study of the chaos structure and the controlled regularization of chaotic processes. In this paper, by using differentially-geometric techniques of trajectory control and non-interacting strategy, attractivity of an orbit belonging to the conditional attractor is provided, and stable regular oscillations of the system are generated. To avoid the lack of analytical description of conditional attractors, a special procedure is proposed which implies the use of invariant hyperplanes tangent to the unknown attractors.