Towards Analytical Chaotic Evolutions in Brusselators / by Albert C.J. Luo, Siyu Guo.

Format:

Book

Author/Creator:

Luo, Albert C.J., Author.

Guo, Siyu., Author.

Series:

Synthesis Lectures on Mechanical Engineering, 2573-3176

Language:

English

Subjects (All):

Engineering.

Electrical engineering.

Engineering design.

Microtechnology.

Microelectromechanical systems.

Technology and Engineering.

Electrical and Electronic Engineering.

Engineering Design.

Microsystems and MEMS.

Local Subjects:

Technology and Engineering.

Electrical and Electronic Engineering.

Engineering Design.

Microsystems and MEMS.

Physical Description:

1 online resource (XIII, 94 p.)

Edition:

1st ed. 2020.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2020.

Summary:

The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université 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���� + 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.

Contents:

Preface

Introduction

Generalized Harmonic Balance Method

Analytical Periodic Evolutions

Analytical Routes to Chaotic Evolutions

Independent Periodic Evolutions

Production and Compensation

References

Authors' Biographies.

ISBN:

9783031796616

3031796616