Global bifurcation approximation of feedback controlled
chaotic systems
Byoung-Cheon Lee, Bong-Gyun Kim and Bo-Hyeun Wang
Information Technology Lab.,
LG Electronics Research Center, 137-140, Seoul, Korea
The control bifurcation(CB) phenomenon and its universality appearing in feedback controlled chaotic systems were described in our previous work[1]. Automatic searching, stabilization and tracking of an UPO were also demonstrated using return map control and adaptive tracking together. In this paper we show that chaotic attractors can be induced from a periodic system with feedback control. Applying feedback control along the direction to chaos, we amplify small experimental errors of the periodic system and generate chaotic attractors. The route from the periodic orbit to the chaotic attractors also shows bifurcation phenomenon and has the same scaling property.
Compared with the conventional local linear approximation nearby an UPO, CB approach can be said a global bifurcation approximation over the whole dynamical range, and it provides us with a systematic methodology for the control of chaotic systems.