Tracking sustained oscillations in delay model oregonators

Abstract

Sustained oscillations occur in many biological organisms and some chemical reactions. Belousov-Zhabotinskii (BZ) reaction is one these chemical oscillators, however, since its oscillatory behaviour is analogous to ones in observed in many biological systems, BZ reaction is often considered as a prototype for bio-chemical oscillators. In this work, by considering a delay model of the Oregonator, which covers the sustained oscillatory mechanism of BZ reaction, we presented some qualitative results in order to find a domain in parameter space that ensures the presence of sustained oscillations. By using the unique positive equilibrium of the model, some necessary and/or sufficient results presented to describe its asymptotic behaviour. Then, by using these results, some numerical computations are presented to describe an oscillatory occurence domain in the parameter space.