Towards Analytical Chaotic Evolutions in Brusselators
暫譯: 朝向布魯塞爾器中的分析性混沌演化
Luo, Albert C. J., Guo, Siyu
- 出版商: Morgan & Claypool
- 出版日期: 2020-05-13
- 售價: $2,250
- 貴賓價: 9.5 折 $2,138
- 語言: 英文
- 頁數: 108
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1681738260
- ISBN-13: 9781681738260
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商品描述
The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Universit Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are:
- analytical routes of periodical evolutions to chaos and
- independent period-(2
商品描述(中文翻譯)
布魯塞拉模型(Brusselator)是一種自催化反應的數學模型,由伊利亞·普里戈金(Ilya Prigogine)及其在布魯塞爾自由大學(Universit Libre de Bruxelles)的合作者提出。布魯塞拉模型的動力學為自催化的振盪化學反應提供了一種振盪反應機制。布魯塞拉模型是一個慢-快振盪化學反應系統。傳統的分析方法無法提供這種慢-快振盪反應的解析解,而數值模擬也無法全面呈現布魯塞拉模型中的週期性演化。在本書中,採用了廣義諧波平衡方法來獲得布魯塞拉模型在諧波擴散下的週期性演化的解析解。通過頻率-振幅特徵,展示了布魯塞拉模型從週期-1運動到混沌的分岔樹,這些特徵可以在頻率域中測量。本書中提出的兩個主要結果是:
- 週期性演化到混沌的解析路徑
- 獨立的週期-(2