ON CONTROLLING A CHAOTIC SYSTEM

Abstract

The use of active (feedback) control to alter the bifurcation structure of dynamical systems is discussed and illustrated with an example. It is shown that with the use of a feedback controller effecting small perturbations in the boundary conditions, one can stabilize some of the otherwise non-stable orbits embedded in the chaotic attractor. The controller also can be used to destabilize stable flows or, in other words, to induce chaos in otherwise laminar (fully predictable), non-chaotic flow. Finally, the controller can be used to switch at will from one flow pattern to another.