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

Hakki Ulas Unal (1) , Islam Boussaada (1, 2, 3) , Silviu-Iulian Niculescu (1, 3)

1 L2S - Laboratoire des signaux et systèmes
2 IPSA - Institut Polytechnique des Sciences Avancées
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

Belousov-Zhabotinskii reaction is a complicated chemical oscillator exhibits temporal and spatiotemporal behaviours that quantitatively match some rhythmic behaviours in biological systems. Its important features are covered by a simple irreversible mechanism, called the Oregonator. By taking into account the physical constraints and to describe the mechanism with a fewer variables, two-delays Oregonator based model is considered in order to investigate the delay effects in chemical reactions exhibiting sustained oscillations. It is shown that the solutions of the model, obtained by use of the delay-mass action kinetics, are positive and bounded. By utilizing the asymptotic stability properties of the model which exhibits positive and bounded solutions, a positive invariant set for the solutions is described. Numerical results are presented to compare with the existing solutions which are qualitatively matches with the experimental results.

Keywords: Sustained oscillation; Delayed Neg- ative Feedback; Oregonator; Chemical Oscillator

Domains: Automatic; Dynamical Systems [math.DS]

Hakki Ulas Unal, Islam Boussaada, Silviu-Iulian Niculescu. A Delay-Based Sustained Chemical Oscillator: Qualitative Analysis of Oregonator-Based Models. IEEE Life Sciences Letters, 2017, 3 (3), pp.9 - 12. ⟨10.1109/LLS.2017.2756834⟩. ⟨hal-01656725⟩