Tracking Sustained Oscillations in Delay Model Oregonators

Hakki Ulaş Ünal 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.
Type de document :
Communication dans un congrès
2016 IEEE Conference on Control Applications(CCA), Sep 2016, Buenos Aires, Argentina. 〈10.1109/cca.2016.7587993 〉
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01658325
Contributeur : Islam Boussaada <>
Soumis le : jeudi 7 décembre 2017 - 15:15:41
Dernière modification le : jeudi 5 avril 2018 - 12:30:13

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Hakki Ulaş Ünal, 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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