PBC-based pulse stabilization of periodic orbits

• We give a rigorous approach to periodic control of periodic discrete systems.
• Stability domains help to choose a suitable control for every particular application.
• Destabilizing bifurcations are prevented.
• We give applications for biological and physical models.

We investigate prediction based schemes to stabilize periodic solutions to potentially chaotic systems of periodic difference equations using pulses at times being a multiple of the period. By introducing the concept of a stability domain, we obtain precise information on the possibility to stabilize given solutions, to avoid destabilizing bifurcations, as well as on the magnitude of the required control.