布雷-李布哈佛斯基反应的数学模型

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-05-29 DOI:10.1098/rspa.2023.0964
Heath Dimsey, Lawrence K. Forbes, Andrew P. Bassom, Courtney Quinn
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引用次数: 0

摘要

众所周知,被广泛研究的布雷-李布哈佛斯基反应通常表现出复杂的化学特性。人们提出了许多数学体系来描述这一过程中发生的碘振荡。最近,有人提出了布雷-利布哈夫斯基反应的四变量模型,分析和数值研究表明可能存在混沌解。我们在此重新审视了这一四变量模型,并对这一系统进行了首次详细研究。我们认为,这个模型也许并不混乱。在这些新见解的启发下,我们在四变量系统的基础上提出了一个简化的双变量模型。建立该模型的双重目标是:既能简化数学分析,又能保留基本的化学机制。我们能够证明,与实际参数值的完整模型相比,我们的简化问题表现非常出色。特别是,我们确定了参数空间的关键区域,在这些区域内可能会出现时间振荡。此外,这些持续振荡与现有的定性实验观测结果是一致的。
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A mathematical model of the Bray–Liebhafsky reaction

It is known that the widely studied Bray–Liebhafsky reaction typically exhibits complex chemical behaviour. Numerous mathematical systems have been proposed to describe the iodine oscillations that occur during this process. Recently, a four-variable model of the Bray–Liebhafsky reaction has been proposed and analytical and numerical investigations suggested that chaotic solutions may exist. We revisit this four-variable model here and perform what appears to be the first detailed work on this system. We suggest that this model is perhaps not chaotic after all. Informed by these fresh insights, we propose a reduced two-variable model based upon the four-variable system. This model is created with the twin goals of enabling simpler mathematical analysis while retaining the underlying chemical mechanisms. We are able to demonstrate that our reduced problem performs very well when compared with the full model for realistic parameter values. In particular, key regions of parameter space are identified within which temporal oscillations can occur. Moreover, these persistent oscillations are consistent with the available qualitative experimental observations.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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