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Volume 4

Series Editors Alain Destexhe Unit´e de Neurosciences Int´egratives et Computationnelles (UNIC) CNRS Gif-sur-Yvette France Romain Brette Equipe Audition (ENS/CNRS) ´ D´epartement d’Etudes Cognitives ´ Ecole Normale Sup´erieure Paris France

For other titles published in this series, go to http://www.springer.com/series/8164

D. Alistair Steyn-Ross · Moira Steyn-Ross Editors

Modeling Phase Transitions in the Brain

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Editors D. Alistair Steyn-Ross Department of Engineering Hillcrest Road University of Waikato Hamilton 3240 Gate 8 New Zealand [email protected]

Moira Steyn-Ross Department of Engineering Hillcrest Road University of Waikato Hamilton 3240 Gate 8 New Zealand [email protected]

Cover design shows brain electrical activity recorded from the cortex of a cat transiting from slow-wave sleep (SWS) into rapid-eye-movement (REM) sleep. The folded grid illustrates a mathematical model for the transition, with SWS and REM phases corresponding to quiescent (lower branch) and activated (upper branch) brain states. [Cat time-series adapted from Destexhe, A., Contreras, D., Steriade, M.: J. Neurosci. 19, 4595–4608 (1999), reproduced with permission, Society for Neuroscience. Sleep manifold adapted from Steyn-Ross, D.A., Steyn-Ross, M.L., Sleigh, J.W., Wilson, M.T., Gillies, I.P., Wright, J.J.: J. Biol. Phys. 31, 547–569 (2005).]

ISBN 978-1-4419-0795-0 e-ISBN 978-1-4419-0796-7 DOI 10.1007/978-1-4419-0796-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009941302 c Springer Science+Business Media, LLC 2010  All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. While the advice and information in this book are believed to be true and accurate at the date of going to press, 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)

Foreword

Early in the 19th century debates on Darwinian theory of evolution, William James asked the question whether consciousness had biological survival value, such that it might be subject to natural selection. The alternatives he considered were widely held notions that consciousness was either an epi