Understanding Nonlinear Dynamics
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathema
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19 Editors
J.E. Marsden L. Sirovich M. Golubitsky W. Jager F. John (deceased)
Advisor G.1ooss
Texts in Applied Mathematics 1.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
Sirovich: Introduction to Applied Mathematics. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Hale/Kofak: Dynamics and Bifurcations. Chorin/Marsden: A Mathematical Introduction to Fluid Mechanics, 3rd ed. HubbardlWest: Differential Equations: A Dynamical Systems Approach: Part I: Ordinary Differential Equations. Sontag: Mathematical Control Theory: Deterministic Finite Dimensional Systems. Perko: Differential Equations and Dynamical Systems. Seaborn: Hypergeometric Functions and Their Applications. Pipkin: A Course on Integral Equations. Hoppensteadt/Peskin: Mathematics in Medicine and the Life Sciences. Braun: Differential Equations and Their Applications, 4th ed. Stoer/Bulirsch: Introduction to Numerical Analysis, 2nd ed. Renardy/Rogers: A First Graduate Course in Partial Differential Equations. Banks: Growth and Diffusion Phenomena: Mathematical Frameworks and Applications. Brenner/Scott: The Mathematical Theory of Finite Element Methods. Van de Velde: Concurrent Scientific Computing. Marsden/Ratiu: Introduction to Mechanics and Symmetry. HubbardIWest: Differential Equations: A Dynamical Systems Approach: Higher Dimensional Systems. Kaplan/Glass: Understanding Nonlinear Dynamics. Holmes: Introduction to Perturbation Methods. Curtain/Zwart: An Introduction to Infinite Dimensional Linear Systems Theory.
Daniel Kaplan Leon Glass
Understanding Nonlinear Dynamics
With 294 Illustrations
Springer Science+Business Media, LLC
Daniel Kaplan Leon Glass Department ofPhysiology McGill University 3655 Drummond Street Montreal, Quebec, Canada H3G lY6
Series Editors J.E. Marsden Department of Mathematics University of California Berkeley, CA 94720 USA M. Golubitsky Department of Mathematics University of Houston Houston, TX 77004 USA
L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA
w. Jăger
Department of Applied Mathematics Universităt Heidelberg Im Neuenheimer Feld 294 69120 Heidelberg, FRG
Mathematics Subject Classifications (1991): 39xx, 92Bxx, 35xx
Library of Congress Cataloging-in-Publication Data Kaplan, Daniel, 1959Understanding nonlinear dynamics I Daniel Kaplan and Leon Glass. p. cm. - (Texts in applied mathematics; 19) Includes bibliographica1 references and index. ISBN 978-0-387-94440-1 ISBN 978-1-4612-0823-5 (eBook) DOI 10.1007/978-1-4612-0823-5 1. Dynamics. 2. Nonlinear theories. 1. G1ass, Leon, 1943-. II. Title. III. Series. QA845.K36 1995b 94-23792 003~85-dc20
Printed on aeid-free paper. © 1995 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 1995 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly ana1ysis
