How to obtain extreme multistability in coupled dynamical systems.

We present a method for designing an appropriate coupling scheme for two dynamical systems in order to realize extreme multistability. We achieve the coexistence of infinitely many attractors for a given set of parameters by using the concept of partial synchronization based on Lyapunov function stability. We show that the method is very general and allows a great flexibility in choosing the coupling. Furthermore, we demonstrate its applicability in different models, such as the Rössler system and a chemical oscillator. Finally we show that extreme multistability is robust with respect to parameter mismatch and, hence, a very general phenomenon in coupled systems.