Switching between orbits in a periodic window

This paper shows the use of chaos control techniques within a periodic window making use of the fact that the infinite variety of unstable periodic orbits coexist with a stable periodic orbit.

Abstract

This paper shows the use of chaos control techniques within a periodic window making use of the fact that the infinite variety of unstable periodic orbits coexist with a stable periodic orbit. The original stable periodic orbit can be distorted into a chaoslike state induced by small external excitations. When this perturbed state approaches an unstable periodic orbit of the original system, control methods can be applied to stabilize the system onto the particular orbit. This technique is applied in the period-3 window of the logistic map using constant excitations and a self-locating control scheme.