A Delay-Based Sustained Chemical Oscillator: Qualitative Analysis of Oregonator-Based Models

The Belousov-Zhabotinsky (BZ) reaction is a complex chemical reaction exhibiting sustained oscillations observed in some real biological oscillators. However, its oscillatory behavior is represented by a simple mechanism, called the Oregonator. Since delay induces unexpected behaviors, the dynamics in BZ reaction in the presence of delays has not been sufficiently addressed. In order to understand the effects induced by the delay parameter in the reaction, by using a two-delay Oregonator-based model, we address the qualitative properties (positivity, boundedness, and stability) of the model in terms of delayed-concentration and delayed-activation. Numerical results are presented to verify the properties of the model described by a qualitative/quantitative analysis.