Asymptotic limit-cycle analysis of oscillating chemical reactions |
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Authors: | Brizard Alain J Berry Samuel M |
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Institution: | 1.Department of Physics, Saint Michael’s College, Colchester, VT, 05439, USA ;2.Department of Chemistry, Saint Michael’s College, Colchester, VT, 05439, USA ; |
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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 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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