Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions
Abstract
The asymptotic limit-cycle analysis of mathematical models for oscillating chemical reactions is presented. In this work, after a brief presentation of mathematical preliminaries applied to the biased Van der Pol oscillator, we consider a two-dimensional model of the Chlorine dioxide Iodine Malonic-Acid (CIMA) reactions and the three-dimensional and two-dimensional Oregonator models of the Belousov-Zhabotinsky (BZ) reactions. Explicit analytical expressions are given for the relaxation-oscillation periods of these chemical reactions that are accurate within 5\% of their numerical values. In the two-dimensional CIMA and Oregonator models, we also derive critical parameter values leading to canard explosions and implosions in their associated limit cycles.
Keywords
Cite
@article{arxiv.2105.01234,
title = {Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions},
author = {Alain J. Brizard and Samuel M. Berry},
journal= {arXiv preprint arXiv:2105.01234},
year = {2021}
}
Comments
15 pages, 24 figures