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thematical Approaches to Biological Systems Networks, Oscillations, and Collective Motions

Mathematical Approaches to Biological Systems

Toru Ohira • Tohru Uzawa Editors

Mathematical Approaches to Biological Systems Networks, Oscillations, and Collective Motions

123

Editors Toru Ohira Graduate School of Mathematics Nagoya University Nagoya, Aichi, Japan

ISBN 978-4-431-55443-1 DOI 10.1007/978-4-431-55444-8

Tohru Uzawa Graduate School of Mathematics Nagoya University Nagoya, Aichi, Japan

ISBN 978-4-431-55444-8 (eBook)

Library of Congress Control Number: 2015935193 Springer Tokyo Heidelberg New York Dordrecht London © Springer Japan 2015 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Japan KK is part of Springer Science+Business Media (www.springer.com)

Preface

Mathematical approaches to biological systems are now fast-growing research endeavors. Although mathematics has traditionally found more applications to physics, many of the same techniques and concepts developed are increasing our abilities for exploring various aspects of biological systems. The aim of this book is to present some aspects of these mathematical approaches under the keywords of “networks”, “oscillations”, and “collective behaviors”. Although each of these subjects is often discussed in separate texts, we hope that readers can sense their mutual connections in concepts. Another feature of this collection is its connection to traditional Japanese research in the related areas. All of the seven chapters carry the tradition of Japanese research of mathematics, engineering, and physics, educated and/or influenced by schools of such pioneering researchers as E. Teramoto, R. Kubo, Y. Kuramoto, S. Amari, K. Kaneko, and S. Oishi. Readers can enjoy the way that unique cultural tones and approaches in research have been passed down. Robert Brown was a botanist interested in the movements of particles observed using a microscope. His original intention was to find ba