Controlling chaotic oscillations in delay-differential systems via peak-to-peak maps

A method for controlling chaotic oscillations in delay differential systems is presented. The method, which is intrinsically heuristic, relies on the capability of predicting the peak (relative maximum) of an output variable from the knowledge of the previous peak. This property, called peak-to-peak dynamics, is owned by several finite-dimensional systems, and crucially relies on the low-dimensionality of the chaotic attractor. In this paper it is shown that even delay-differential systems may display peak-to-peak dynamics, and the conditions giving rise to this property are analyzed. Then, a reduced model (a first-order map) derived via peak-to-peak dynamics is exploited to suppress chaos in favor of a periodic regime.