Bifurcation Theory and Bistability
In this chapter, we will recapitulate the essential concepts, definitions and theorems of the Lyapunov and Andronov stability theories of dynamical systems. The global aim is to prepare the reader for the mathematical abstraction of biological switches an
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Hamid Reza Noori
Hysteresis Phenomena in Biology
123
SpringerBriefs in Applied Sciences and Technology Mathematical Methods
Series editor Anna Marciniak-Czochra, Heidelberg, Germany
For further volumes: http://www.springer.com/series/11219
Hamid Reza Noori
Hysteresis Phenomena in Biology
123
Hamid Reza Noori Central Institute for Mental Health Institute for Psychopharmacology Mannheim Germany
ISSN 2191-530X ISBN 978-3-642-38217-8 DOI 10.1007/978-3-642-38218-5
ISSN 2191-5318 (electronic) ISBN 978-3-642-38218-5 (eBook)
Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013955060 The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
We should be careful to get out of an experience only the wisdom that is in it—and stop there. Mark Twain
Preface
For over a century, nonlinear phenomena of hysteresis type have been ubiquitous in different areas of science and technology from the physics of materials to the meta-physics of the human behavior. However, mathematical approaches to investigate biological processes with hysteresis nonlinearities have a much shorter history. Although the idea of modeling chemical and biological systems with multiple steady states and state transition dynamics (switches) goes back t
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