Relaxation oscillations and canards of a regulated two–gene model

P. De Maesschalck; G. Kiss; A. Kovacs

doi:10.1016/j.jmaa.2021.125144

Relaxation oscillations and canards of a regulated two–gene model

P. De Maesschalck
, G. Kiss
, A. Kovacs

Mathematical Sciences Research Centre

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1 Citation (Scopus)

135 Downloads (Pure)

Abstract

We investigate a two–gene system with an autoregulatory feedback loop using geometric singular perturbation theory. We identify (coexisting) relaxation oscillations, singular Hopf bifurcations, homoclinic loops etc. We also demonstrate a new method to compute the criticality of the singular Hopf bifurcations.

Original language	English
Article number	125144
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	502
Issue number	1
Early online date	20 Mar 2021
DOIs	https://doi.org/10.1016/j.jmaa.2021.125144
Publication status	Published - 01 Oct 2021

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Relaxation oscillations and canards of a regulated two–gene model
Copyright 2021 Elsevier. This manuscript is distributed under a Creative Commons Attribution-NonCommercial-NoDerivs License (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited.
Accepted author manuscript, 1.62 MBLicence: CC BY-NC-ND

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AB - We investigate a two–gene system with an autoregulatory feedback loop using geometric singular perturbation theory. We identify (coexisting) relaxation oscillations, singular Hopf bifurcations, homoclinic loops etc. We also demonstrate a new method to compute the criticality of the singular Hopf bifurcations.

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Relaxation oscillations and canards of a regulated two–gene model

Abstract

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