Tracking Sustained Oscillations in Delay Model Oregonators

Hakki Ulaş Unal 1 Islam Boussaada 2, 3, 4 Silviu-Iulian Niculescu 4
4 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
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.
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Hakki Ulaş Unal, Islam Boussaada, Silviu-Iulian Niculescu. Tracking Sustained Oscillations in Delay Model Oregonators. 2016 IEEE Conference on Control Applications(CCA), Sep 2016, Buenos Aires, Argentina. ⟨10.1109/cca.2016.7587993 ⟩. ⟨hal-01658325⟩



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