Neural Networks with Discontinuous/Impact Activations
This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments
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Marat Akhmet Enes Yılmaz
Neural Networks with Discontinuous/ Impact Activations
Nonlinear Systems and Complexity Series Editor Albert C.J. Luo Southern Illinois University Edwardsville, IL, USA
For further volumes: http://www.springer.com/series/11433
Marat Akhmet • Enes Yılmaz
Neural Networks with Discontinuous/Impact Activations
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Marat Akhmet Department of Mathematics Middle East Technical University (METU) Üniversiteler Mah. Dumlupinar Ankara, Turkey
Enes Yılmaz Department of Mathematics Adnan Menderes University Merkez Kampüsü Aytepe Mevkii Aydın, Turkey
ISSN 2195-9994 ISSN 2196-0003 (electronic) ISBN 978-1-4614-8565-0 ISBN 978-1-4614-8566-7 (eBook) DOI 10.1007/978-1-4614-8566-7 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013951645 © Springer Science+Business Media New York 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)
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Preface
This book addresses the new models in mathematical neuroscience and artificial neural networks, which have many similarities with the structure of the human brain and the functions of cells by electronic circuits. The networks have been investigated due to their extensive applications in classification of patterns, associative memories, image processing, arti
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