Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions
| Autor: | Samuel M. Berry, Alain J. Brizard |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Chemical Physics (physics.chem-ph) Work (thermodynamics) Van der Pol oscillator Mathematical model Applied Mathematics FOS: Physical sciences General Chemistry Mathematical Physics (math-ph) 010402 general chemistry Chemical reaction 01 natural sciences Limit cycle analysis 010305 fluids & plasmas 0104 chemical sciences Critical parameter Physics - Chemical Physics 0103 physical sciences Limit (mathematics) Statistical physics Oregonator Mathematical Physics |
| DOI: | 10.48550/arxiv.2105.01234 |
| Popis: | 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. Comment: 15 pages, 24 figures |
| Databáze: | OpenAIRE |
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