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 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.
Highlights
Oscillating chemical reactions have attracted attention since their first announcement [1, 2]
By 1972, increased interest in chemical oscillators came from papers puiblished by Field et al [4] and Winfree [5], among others, detailing a more complete mechanism of the BZ reaction and chemical reaction-diffusion systems, respectively
II, we present the mathematical preliminaries associated with the type of coupled first-order differential equations considered in our work
Summary
Oscillating chemical reactions have attracted attention since their first announcement [1, 2]. The purpose of the present paper is to perform a unified asymptotic analysis of two well-known oscillating chemical reactions: The Chlorine dioxide Iodine Malonic-Acid (CIMA) reaction and the Oregonator model of the Belousov-Zhabotinsky (BZ) reactions. In the two Sections, we focus our attention on two well-known paradigm models for oscillatory chemical reactions: the Chlorine dioxide Iodine Malonic-Acid (CIMA) reactions (Sec. IV) and the Oregonator model of the Belousov-Zhabotinsky (BZ) reactions (Sec. V), presented first as a three-variable model (Oregonator-3) and reduced to a two-variable model (Oregonator-2).
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