Towards Analytical Chaotic Evolutions in Brusselators (Synthesis Lectures on Materials and Optics) - Hardcover

Luo, Albert C.J.; Guo, Siyu

9781681738260: Towards Analytical Chaotic Evolutions in Brusselators (Synthesis Lectures on Materials and Optics)

Hardcover

ISBN 10: 1681738260 ISBN 13: 9781681738260

Verlag: Morgan & Claypool Publishers, 2020

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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-(2𝑙 1) evolution to chaos.

This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.

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