Engel, Maximilian and Olicón-Mendez, Guillermo
(2023)
*A singular perturbation analysis for the Brusselator.*
Preprint
.
(Submitted)

Full text not available from this repository.

Official URL: https://doi.org/10.48550/arXiv.2311.00575

## Abstract

In this work we study the Brusselator - a prototypical model for chemical oscillations - under the assumption that the bifurcation parameter is of order O(1/ϵ) for positive ϵ≪1. The dynamics of this mathematical model exhibits a time scale separation visible via fast and slow regimes along its unique attracting limit cycle. Noticeably this limit cycle accumulates at infinity as ϵ→0, so that in polar coordinates (θ,r), and by doing a further change of variable r↦r−1, we analyse the dynamics near the line at infinity, corresponding to the set {r=0}. This object becomes a nonhyperbolic invariant manifold for which we use a desingularising rescaling, in order to study the closeby dynamics. Further use of geometric singular perturbation techniques allows us to give a decomposition of the Brusselator limit cycle in terms of four different fully quantified time scales.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3066 |

Deposited By: | Jana Jerosch |

Deposited On: | 05 Feb 2024 12:57 |

Last Modified: | 05 Feb 2024 12:57 |

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