Simulation of biological oscillators involving large time delays

Many biological systems exhibit periodic or rhythmic behaviour. Some mathematical models proposed for this class of systems involve an on-off relay followed by a large time delay within a feedback structures. This paper presents a method for simulating the relay-delay combination exactly without invoking any approximations for the delays. The method is then used to simulate respiratory and cardiovascular systems whose models involve relays and large time delays. Possible synchronization of these two oscillations due to coupling between the two systems is also experimentally investigated.