A Framework for Engineering the Collective Behavior of Complex Rhythmic Systems.

We have developed an engineering framework which utilizes experiment-based phase models to tune complex dynamic structures to desired states; weak, non-destructive signals are employed to alter interactions among nonlinear rhythmic elements. In this manuscript we present an integrated overview and discussion of our recent studies in this area. Experiments on electrochemical reactions were conducted using multi-electrode arrays to demonstrate the use of mild model-engineered feedback to achieve a desirable system response. Application is made to the tuning of phase difference between two oscillators, generation of sequentially-visited dynamic cluster patterns, engineering dynamically differentiated cluster states, and to the design of a nonlinear anti-pacemaker for the destruction of synchronization of a population of interacting oscillators.