Qualitative resonance of feedback-controlled chaotic oscillators

The qualitative resonance of feedback-controlled chaotic oscillators is the ability of the control system to qualitatively synchronize with a reference signal similar to one of the unstable periodic orbits embedded in the open-loop attractor. This property, discovered by O. De Feo (2004a; 2004b) while studying Shilnikov-type attractors, was explained in terms of the random-like rephasing mechanism characterizing the oscillator's dynamics, so to guarantee the eventual in-phase looking with the reference forcing. We experimentally show that the phenomenon works more in general, even in the absence of a rephasing mechanism. Intuitively, the forcing by the target cycle, or by a qualitative approximation of it, is sufficient to bring in the in-phase condition. Our results can make chaos control more practicable than so far imagined, as a qualitative control can be achieved with no a-priori knowledge about the target solution.