Collective organization, such as rhythmic patterns and synchronized states, is commonly found in complex systems composed of a large number of interacting oscillatory elements. Such behavior is important in biological functions such as circadian rhythm and memory as well as in epilepsy and essential tremors. A major question of both theoretical and practical importance is how to bring these dynamical systems to a desired state or, equivalently, how to avoid a deleterious state without destroying the inherent rhythmic behavior of the individual elements.

We have developed a general methodology for engineering the collective emergent behavior of rhythmic systems by using a weak non-linear feedback signal to gently steer the system to a desired state. Flexibility is obtained through the use of experiment-based reduced models in designing the feedback. Such models capture the essential dynamical behavior of the system without requiring detailed chemical or biological descriptions of the individual rhythmic units.

We have experimentally demonstrated the effectiveness of the method by engineering the collective behavior of a population of oscillatory electrochemical elements. Application is made to the design of a nonlinear anti-pacemaker for the destruction of pathological synchronization of a population of interacting oscillators and to the generation of sequentially-visited dynamic cluster patterns similar to reproducible sequences seen in biological systems.