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arXiv · 2105.01234

Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions

Alain J. Brizard·Samuel M. Berry
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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.

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Alain J. Brizard, Samuel M. Berry. 2021-05-04. Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions. https://arxiv.org/abs/2105.01234

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