Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions

TL;DR

This paper analyzes the asymptotic behavior of oscillating chemical reactions using mathematical models, providing explicit formulas for oscillation periods and identifying critical parameters for complex dynamical phenomena.

Contribution

It introduces explicit analytical expressions for oscillation periods and critical parameters for canard phenomena in chemical reaction models.

Findings

Explicit formulas for relaxation-oscillation periods within 5% accuracy.

Identification of parameter values leading to canard explosions and implosions.

Application to CIMA and Oregonator models of BZ 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.