Further remarks on delay dynamics in Oregonator models

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

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

Motivated by the fact that molecules reacting through some biological channels may need some time-lag due transcription and translation processes, this note is devoted to the study of stability properties of a delayed Oregonator model. In this work, we consider an Oregonator based model consisting of two different delays, which origin the time needed to reach the chemical equilibrium and regeneration of certain chemical variable used as a negative feedback. Positive equilibrium points as well as the stability of solutions in their neighborhood are investigated. Furthermore, Hopf bifurcation points and their crossing frequencies are further discussed.

Domaines: Automatique / Robotique; Systèmes dynamiques [math.DS]

Unal Hakki, Islam Boussaada, Silviu-Iulian Niculescu. Further remarks on delay dynamics in Oregonator models. IEEE International Conference on Control and Automation, Jun 2016, Kathmandu, Nepal. ⟨10.1109/ICCA.2016.7505261⟩. ⟨hal-01445899⟩