Differential delay equations in chemical kinetics. Nonlinear models: The cross-shaped phase diagram and the Oregonator

Abstract

Delayed feedback plays a key role in most, if not all chemical oscillators. We derive general results useful in the linear stability analysis of models that explicitly incorporate delay by using differential delay equations. Two models of nonlinear chemical oscillators, the cross-shaped phase diagram model of Boissonade and De Kepper and the Oregonator, are modified by deleting a feedback species and mimicking its effect by a delay in the kinetics of another variable. With an appropriate choice of the delay time, the reduced models behave very much like the full systems. It should be possible to carry out similar reductions on more complex mechanisms of oscillating reactions, thereby providing insight into the role of delayed feedback in these systems.