PDE Methods for Two-Dimensional Neural Fields
We consider neural field models in both one and two spatial dimensions and show how for some coupling functions they can be transformed into equivalent partial differential equations (PDEs). In one dimension we find snaking families of spatially-localised
- PDF / 11,870,983 Bytes
- 488 Pages / 439.42 x 683.15 pts Page_size
- 38 Downloads / 252 Views
Fields
Theory and Applications
Neural Fields
Stephen Coombes • Peter beim Graben • Roland Potthast • James Wright Editors
Neural Fields Theory and Applications
123
Editors Stephen Coombes School of Mathematical Sciences University of Nottingham Nottingham, United Kingdom
Roland Potthast Department of Mathematics University of Reading Reading, United Kingdom
Peter beim Graben Department of German Studies and Linguistics Humboldt-UniversitRat zu Berlin Berlin, Germany James Wright School of Medicine University of Auckland Auckland, New Zealand
ISBN 978-3-642-54592-4 ISBN 978-3-642-54593-1 (eBook) DOI 10.1007/978-3-642-54593-1 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014942371 © Springer-Verlag Berlin Heidelberg 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)
Preface
The Neural Field: A Framework for Brain Data Integration? This book presents a perspective on the advancing subject of neural fields—that is, theories of brain organization and function in which the interaction of billions of neurons is treated as a continuum. The intention is to reduce the enormous complexity of neuronal interactions to simpler, population properties that are tractable by analytical mathematical tools. By so doing, it is hoped t
Data Loading...
