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Belairglassch2-1997 Interdisciplinary Applied Mathematics Volume 25 Editors S.S.Antman J.E. Marsden L. Sirovich S. Wiggins Geophysics and Planetary Sciences Mathematical Biology L. Glass, J.D. Murray Mechanics and Materials R.V.Kohn Systems and Control S.S. Sastry, P.S. Krishnaprasad Problems in engineering, computational science, and the physical and biologica! sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines bas led to the establishment ofthe series: Interdisciplinary Applied Mathematics. The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, frrstly, by encouraging the ways that that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications; and, secondly, by encouraging other scientific disciplines to engage in a dialog with mathernaticians outlining their problems to both access new methods and suggest innovative developments within mathernatics itself. The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology. Interdisciplinary Applied Mathematics Volumes published are listed at the end of the book. Springer Science+Business Media, LLC Anne Beuter Leon Glass Michael C. Mackey Michele S. Titcombe Editors Nonlinear Dynamics in Physiology and Medicine With 162 Illustrations ~Springer Anne Beuter Leon Glass Institut de Biologie Department of Physiology Universite de Montpellier 1 McGill University 4, Boulevard Henri IV Montreal, Quebec H3G 1Y6 Montpellier Cedex 1, 34060 Canada France [email protected] [email protected] Michael C. Mackey Micbe1e S. Titcombe Department of Physiology Department of Physio1ogy McGill University McGill University Montreal, Quebec H3G 1Y6 Montreal, Quebec H3G 1Y6 Canada Canada [email protected] [email protected] Editors s.s. Antman J.E. Marsden Department of Mathematics Control and Dynamical Systems and Mai! Code 107-81 Institute for Physical Science and Technology California Institute ofTechno1ogy University ofMaryland Pasadena, CA 91125 College Park, MD 20742 USA USA [email protected] [email protected] L. Sirovich S. Wiggins Division of Applied Mathematics School ofMathematics Brown University University of Bristol Providence, RI 02912 Bristol BSS 1TW USA UK [email protected] [email protected] Mathematics Subject Classification (2000): 92Cxx, 37-01 Library of Congress Cata1oging-in-Publication Data Nonlinear dynarnics in physiology and medicine 1 editors, Anne Beuter ... [et al.]. p. cm-(Interdisciplinary applied mathematics ; v.25) lncludes bibliographical references and index. 1. Physiology-Mathematical models. 2. Nonlinear systerns. 3. Dynarnics. l. Beuter, Anne. Il. Series. QP33.6.M36N663 2003 612".001"5118-dc21 2003044936 ISBN 978-1-4419-1821-5 ISBN 978-0-387-21640-9 (eBook) DOI 10.1007/978-0-387-21640-9 © 2003 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 2003 Softcover reprint of the hardcover lst edition 2003 AU rights reserved. This work may not be translated or copied in whole or in part without the written pennission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any forrn of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade narnes, trademarks, service marks, and similar terrns, even if they are not identi­ fied as such, is not tobe taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 SPIN 10911 792 Typesetting: Pages created by the editors using a Springer LaTeX macro package. www.springer-ny.com xii Sources and Credits 3.13 From Nonlinear Dynamics and Chaos by Steven H. Strogatz. Copy­ right @1994. Reprinted by permission of Perseus Book Publishers, a member of Perseus Books, L.L.C. 3.17 Reprinted with permission from Jalife, J., and Antelevitch, C. 1979. Phase resetting and annihilation of pacemaker activity in cardiac tis­ sue. Science, Volume 206, pages 695-697. Copyright @1979 American Association for the Advancement of Science. 3.18 Guevara, M.R., and Jongsma, H.J. 1992. Phase resetting in a model of sinoatrial nodal membrane: Ionic and topologica! aspects. American Journal of Physiology, Volume 258, pages H734-H747. Reprinted by permission of the American Physiological Society. 3.19, 3.20 Guttman, R., Lewis, S., and Rinzel, J. 1980. Control of repetitive firing in squid axon membrane as a model for a neuron os­ cillator. Journal of Physiology (London}, Volume 305, pages 377-395. Reprinted by permission of the Physiological Society and J. Rinzel. 3.21 Guevara, M.R., and Jongsma, H.J. 1992. Phase resetting in a model of sinoatrial nodal membrane: Ionic and topologica! aspects. American Journal of Physiology, Volume 258, pages H734-H747. Reprinted by permission of the American Physiological Society. 3.22 Noma, A., and Irisawa, H. 1975. Effects of Na+ and K+ on the rest­ ing membrane potential of the rabbit sinoatrial node cell. Japanese Journal of Physiology, Volume 25, pages 287-302. Reprinted with permission of the Japanese Journal of Physiology. 3.25, 3.27 Guttman, R., Lewis, S., and Rinzel, J. 1980. Control of repetitive firing in squid axon membrane as a model for a neu­ roneoscillator. Journal of Physiology (London}, Volume 305, pages 377-395. Reprinted by permission of the Physiological Society and J. Rinzel. 3.29 Abraham, R.H., and Shaw, C.D. 1982. Dynamics: The Geometry of Behavior. Reprinted by permission of R.H. Abraham, Aerial Press. 3.30 Yehia, A.R., Jeandupeux, D., Alonso, F., and Guevara, M.R. 1998. Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells. Chaos, Volume 9, pages 916-931. Reprinted by permission of the American Institute of Physics. 3.31 Abraham, R.H., and Shaw, C.D. 1982. Dynamics: The Geometry of Behavior. Reprinted by permission of R.H. Abraham, Aerial Press. 3.32, 3.33 Guevara, M.R., Alonso, F., Jeandupeux, D. and van Ginneken, A.G.G. 1989. Alternans in periodically stimulated isolated ventricular myocytes: Experiment and model. In Cell to Cell Signalling: From Sources and Credits xiii Experiments to Theoretical Models, pages 551-563. Reprinted with permission of M.R. Guevara. 3.34 Kaplan, D.T., Clay, J.R., Manning, T., Glass, L., Guevara, M.R., and Shrier, A. 1996. Subthreshold dynamics in periodically stimulated squid giant axons. Physical Review Letters, Volume 76, pages 4074- 4076. 3.35 Guevara, M.R., and Jongsma, H.J. 1992. Phase resetting in a model of sinoatrial nodal membrane: Ionic and topologica! aspects. American Journal of Physiology, Volume 258, pages H734-H747. Reprinted by permission of the American Physiological Society. 3.37 Panels A and B from Seydel, R. 1994. Prom Equilibrium to Chaos: Practical Bifurcation and Stability Analysis. Reprinted with permission of Springer-Verlag. 3.37 Panels C and D from Abraham, R.H., and Shaw, C.D. 1982. Dy­ namics: The Geometry of Behavior. Reprinted by permission of R.H. Abraham, Aerial Press. 3.38 Abraham, R.H., and Shaw, C.D. 1982. Dynamics: The Geometry of Behavior. Reprinted by permission of R.H. Abraham, Aerial Press. 3.39 Panels A and B from Crutchfield, J., Farmer, D., Packard, N., Shaw, R., Jones, G., and Donnelly, R.J. 1980. Power spectral analysis of a dynamical system. Physical Letters A, Volume 76, pages 1-4, Copyright @1980, with permission of Elsevier. 3.39 Panel C from Olsen, L.F., and Degn, H. 1985. Chaos in biologica! systems. Quarterly Review of Biophysics, Volume 18, pages 165-225. Reprinted with the permission of Cambridge University Press. 3.40 Panels A (left) and B (left) from Abraham, R.H., and Shaw, C.D. 1982. Dynamics: The Geometry of Behavior. Reprinted by permission of R.H. Abraham, Aerial Press. 3.40 Panels A (right), B (right) and C from Seydel, R. 1994. Prom Equilibrium to Chaos: Practical Bifurcation and Stability Analysis. Reprinted with permission of Springer-Verlag. 3.44 Guevara, M.R., and Jongsma, H.J. 1992. Phase resetting in a model of sinoatrial nodal membrane: Ionic and topologica! aspects. American Journal of Physiology, Volume 258, pages H734-H747. Reprinted by permission of the American Physiological Society. 3.45 Guevara, M.R., and Jongsma, H.J. 1992. Phase resetting in a model of sinoatrial nodal membrane: Ionic and topologica! aspects. American Journal of Physiology, Volume 258, pages H734-H747. Reprinted by permission of the American Physiological Society. xiv Sources and Credits 4.2A Hodgkin, A.L., and Keynes, R.D. 1956. Experiments on the injection of substances into squid giant axons by means of a microsyringe. Jour­ nal of Physiology (London}, Volume 131. Reprinted with permission of The Physiological Society. 4.2B Hille, B. 2001. Ionic Channels of Excitable Membranes, Sinauer Sunderland. Reprinted with the permission of Sinauer Associates, Inc. 4.2 Panels C and D from Baker, P.F., Hodgkin, A.L., and Shaw, T.I. 1961. Replacement of the protoplasm of a giant nerve fibre with artificial solutions. Nature, Volume 190 (no. 4779), pages 885-887. Reprinted with permission. 4.3 Nicholls, J.G., Martin, A.R., Wallace, B.G., and Fuchs, P.A. 2001. From Neuron to Brain, Sinauer Sunderland. Reprinted with the permission of Sinauer Associates, Inc. 4.4 Alonso, A., and Klink, R. 1993. Differential responsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II. Jour­ nal of Neurophysiology, Volume 70, pages 128-143.
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