ADAPTIVE STRATEGIES FOR RECOGNITION, NOISE FILTERING, CONTROL, SYNCHRONIZATION AND TARGETING OF CHAOS

Combining knowledge of the local variation rates with some information on the long time trends of a dynamical system, we introduce an adapti ve recognition technique consisting in a sequence of variable resoluti on observation intervals at which the geometrical positions are sample d. The sampling times are chosen so that the sequence of observed poin ts forms a regularized set, in the sense that the separation of adjace nt points is almost uniform. We show how this adaptive technique is ab le to recognize the unstable periodic orbits embedded within 3. chaoti c attractor and stabilize anyone of them even in the presence of noise , through small additive corrections to the dynamics. These techniques have been applied to the synchronization of three chaotic systems, as suring secure communication between a message sender and a message rec eiver; furthermore they provide robust solutions to the problems of ta rgeting of chaos and of filtering the noise out of an experimental cha otic data set. Implementation of adaptive methods to chaotic Lorenz, t hree and four dimensional Roessler models and Mackey-Glass delayed sys tem are reported. (C) 1997 American Institute of Physics.