Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a
- PDF / 22,470,379 Bytes
- 408 Pages / 439.37 x 666.142 pts Page_size
- 69 Downloads / 224 Views
For further volumes: www.springer.com/series/34
Maoan Han r Pei Yu
Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
Maoan Han Department of Mathematics Shanghai Normal University Shanghai, China, People’s Republic
Pei Yu Dept. Applied Mathematics University of Western Ontario London, Ontario, Canada
Additional material to this book can be downloaded from http://extras.springer.com Password: [978-1-4471-2917-2] ISSN 0066-5452 Applied Mathematical Sciences ISBN 978-1-4471-2917-2 e-ISBN 978-1-4471-2918-9 DOI 10.1007/978-1-4471-2918-9 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2012936364 Mathematics Subject Classification: 34C07, 34C20, 34C23, 34D10, 34D20, 34E10, 34E13 © Springer-Verlag London Limited 2012 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
In the past half century, dynamical system theory, also more grandly called “nonlinear science”, has developed rapidly. In particular, the discovery of chaos has revolutionized the field. The study of chaos is closely related to research in the area of bifurcation and stability, and, in particular, the theory of limit cycles has had a significant impact since chaos may be considered to be a summation of motions with an infinite number of frequencies (such as the scenario of “period doubling”, which leads to chaos). Although limit cycles involve a comparatively simple motion, they appear in almost all disciplines of science and engineering including mechanics, aeronautics, electrical circuits, control systems, population problems, economics, financial systems, stock markets, ecological systems, etc. In fact, most of the early work in the theory of limit cycles was stimulated by practical problems displaying periodic behavior. Therefore, the study of the bifurcation of limit cycles is not only significant for its theoretical development, but also plays an importan
