Dynamics of an Electronic Relay Systems with Bandpass Filtered Feedback

Delay dynamics have wide relevance in fundamental science and technology due to the ubiquitous presence of feedback loops in which time lags arise because of natural processes, control interfaces, or performance limits of components. We present results from a well-controlled experiment that is representative of feedback systems with relays (switches) that actuate after a fixed delay. Notably, the system exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of parameters. We then study the system dynamics analytically. The model we consider is a nonsmooth second-order delay differential equation that describes single-input single-output systems in which the delayed feedback is a bandpass filtered relay signal. We discuss how periodic solutions and bifurcations can be obtained by reducing the system to a set of finite-dimensional maps. We find good agreement between theory and experiment.