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An Introduction to Nonlinear Chemical DynamicsOscillations, Waves, Patterns, and Chaos$
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Irving R. Epstein and John A. Pojman

Print publication date: 1998

Print ISBN-13: 9780195096705

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195096705.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 January 2022

Fundamentals

Fundamentals

Chapter:
(p.17) 2 Fundamentals
Source:
An Introduction to Nonlinear Chemical Dynamics
Author(s):

Irving R. Epstein

John A. Pojman

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195096705.003.0007

Before plunging into the meat of our discussions, we will review some basic but necessary ideas. Much of this material will be familiar to many readers, and we encourage you to move quickly through it or to skip it completely if appropriate. If you have not encountered these concepts before, you will find it worthwhile to invest some time here and perhaps to take a look at some of the more detailed references that we shall mention. We begin with a review of chemical kinetics. We then consider how to determine the stability of steady states in an open system using analytical and graphical techniques. Finally, we look at some of the methods used to represent data in nonlinear dynamics. The problems that we are interested in involve the rates of chemical reactions, the study of which forms the basis of chemical kinetics. This is a rich and beautiful subject, worthy of whole volumes. For those interested in a less superficial view than we have room to present here, we recommend several excellent texts on kinetics (Jordan, 1979; Cox, 1994; Espenson, 1995). We review here a minimal set of fundamentals necessary for what comes later.

Keywords:   Arrhenius equation, Brusselator, CSTR, Dushman reaction, Jacobian, Law of Mass Action, Oregonator, Poincare-Bendixson theorem, Roebuck reaction

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