Prediction-based control of chaos and a dynamic Parrondoʼs paradox

We analyze the stabilization of an unstable periodic orbit (UPO) by periodic prediction-based control (PBC). We rigorously prove that, for 2-periodic orbits, a pulse strategy reduces the necessary control strength to stabilize the UPO. Moreover, we find that in some cases the periodic control prevents some undesirable effects induced by the PBC method. In this way, we provide an example of a dynamic Parrondoʼs paradox: the switching between two undesirable dynamics results in a nicely periodic dynamic behavior.