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Nonlinear Dynamics in Biological Systems

Se MA

SEMA SIMAI Springer Series Series Editors: Luca Formaggia • Pablo Pedregal (Editors-in-Chief) • Amadeu Delshams • Jean-Frédéric Gerbeau • Carlos Parés • Lorenzo Pareschi • Andrea Tosin • Elena Vazquez • Jorge P. Zubelli • Paolo Zunino Volume 7

More information about this series at http://www.springer.com/series/10532

Jorge Carballido-Landeira • Bruno Escribano Editors

Nonlinear Dynamics in Biological Systems

123

Editors Jorge Carballido-Landeira Université Libre de Bruxelles Brussels, Belgium

ISSN 2199-3041 SEMA SIMAI Springer Series ISBN 978-3-319-33053-2 DOI 10.1007/978-3-319-33054-9

Bruno Escribano Basque Center for Applied Mathematics Bilbao, Spain

ISSN 2199-305X (electronic) ISBN 978-3-319-33054-9 (eBook)

Library of Congress Control Number: 2016945273 © Springer International Publishing Switzerland 2016 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 This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland

Preface

Many biological systems, such as circadian rhythms, calcium signaling in cells, the beating of the heart and the dynamics of protein folding, are inherently nonlinear and their study requires interdisciplinary approaches combining theory, experiments and simulations. Such systems can be described using simple equations, but still exhibit complex and often chaotic behavior characterized by sensitive dependence on initial conditions. The purpose of this book is to bring together the mathematical bases of those nonlinear equations that govern various important biological processes occurring at different spatial and temporal scales. Nonlinearity is first considered in terms of the evolution equations describing RNA neural networks, with emphasis on analysing population asymptotic states and their significance in biology. In order to achieve a quantitative characterization of RNA fitness landscapes, RNA pr