Chaos in Biological Systems

319 Pages·1987·11.548 MB·English

by  Ary L. Goldberger, Bruce J. West (auth.), H. Degn, A. V. Holden, L. F. Olsen (eds.)

Chaos in
Biological Systems
NATO ASI Series
Advanced Science Institutes Series
A series presenting the results of activities sponsored by the NATO Science Committee,
which aims at the dissemination of advanced scientific and technological knowledge,
with a view to strengthening links between scientific communities.
The series is published by an international board of publishers in conjunction with the
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B Physics New York and London
C Mathematical D. Reidel Publishing Company
and Physical Sciences Dordrecht, Boston, and Lancaster
D Behavioral and Social Sciences Martinus Nijhoff Publishers
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Materials Sciences
F Computer and Systems Sciences Springer-Verlag
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H Cell Biology Paris, and Tokyo
Recent Volumes in this Series
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edited by Nuri Akkas
Volume 133-Membrane Receptors, Dynamics, and Energetics
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Volume 134-Piant Vacuoles: Their Importance in Solute Compartmentation in
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Volume 136-The Molecular Basis of Viral Replication
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Volume 137-DNA-Ligand Interactions: From Drugs to Proteins
edited by Wilhelm Guschlbauer and Wolfram Saenger
Volume 138-Chaos in Biological Systems
edited by H. Degn, A. V. Holden, and L. F. Olsen
Series A: Life Sciences
Chaos in
Biological Systems
Edited by
H. Degn
Odense University
Odense, Denmark
A. V. Holden
The University of Leeds
Leeds, United Kingdom
and
L. F. Olsen
Odense University
Odense, Denmark
Springer Science+Business Media, LLC
Proceedings of a NATO Advanced Research Workshop on
Chaos in Biological Systems,
held December 8-12, 1986,
at Dyffryn House, Cardiff, Wales
Library of Congress Cataloging in Publication Data
NATO Advanced Research Workshop on Chaos in Biological Systems (1986:
Cardiff, South Glamorgan)
Chaos in biological systems.
(NATO ASI series. Series A, Life sciences; vol. 138)
"Proceedings of a NATO Advanced Research Workshop on Chaos in
Biological Systems, held December 8-12, 1986, at Dyffryn House, Cardiff,
Wales"-T.p. verso.
"Published in cooperation with NATO Scientific Affairs Division."
Includes bibliographies and index.
1. Chaotic behavior in systems-Congresses. 2. Physiology-Congresses. I.
Degn, Hans. II. Holden, Arun V., 1947- . Ill. Olsen, L. F. (Lars F.) IV. North
Atlantic Treaty Organization. Scientific Affairs Division. V. Title. VI. Series:
NATO ASI series. Series A, Life sciences; v. 138. [DNLM: 1. Biochemistry
congresses. QU 34 N279c 1986]
QP33.6.C48N38 1986 574 87-7203
ISBN 978-1-4757-9633-9 ISBN 978-1-4757-9631-5 (eBook)
00110.1007/978-1-4757-9631-5
© 1987 Springer Science+Business Media New York
Originally published by Plenum Press, New York in 1987
Softcover reprint of the hardcover 1st edition 1987
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming;
recording, or otherwise, without written permission from the Publisher
PREFACE
In recent years experimental and numerical studies have shown that
chaos is a widespread phenomenon throughout the biological hierarchy
ranging from simple enzyme reactions to ecosystems. Although a coherent
picture of the fundamental mechanisms responsible for chaotic dynamics
has started to appear it is not yet clear what the implications of such
dynamics are for biological systems in general. In some systems it
appears that chaotic dynamics are associated with a pathological condi
tion. In other systems the pathological condition has regular periodic
dynamics whilst the normal non-pathological condition has chaotic dyna
mics. Since chaotic behaviour is so ubiquitous in nature and since the
phenomenon raises some fundamental questions about its implications for
biology it seemed timely to organize an interdisciplinary meeting at
which leading scientists could meet to exchange ideas, to evaluate the
current state of the field and to stipulate the guidelines along which
future research should be directed.
The present volume contains the contributions to the NATO Advanced
Research Workshop on "Chaos in Biological Systems" held at Dyffryn House,
St. Nicholas, Cardiff, U.K., December 8-12, 1986. At this meeting 38
researchers with highly different backgrounds met to present their
latest results through lectures and posters and to discuss the applica
tions of non-linear techniques to problems of common interest.. In spite
of their involvement in the study of chaotic dynamics for several years
many of the participants met here for the first time. As organizers we
feel that the outcome lived up to our expectations, and we should like to
thank all participants for the enthusiasm they carried with them and for
contributing to this volume. We also acknowledge the staff at Dyffryn
House and at the Microbiology Department, University College, Cardiff
for their help in the organization. Special thanks to Mrs. Nia Pagett
for her assistance before, during and after the meeting and Mrs. Lynn
Buckley and Mrs. Jackie Hill, Leeds University for typing the manuscripts.
Finally, we thank the NATO Scientific Affairs Division, Brussels and the
Commission of the European Communities, Directorate-General for Science
Research and Development, Brussels for financial support of the meeting.
Without the joint support from both parties this meeting could not have
been held.
March 1987 Hans Degn
Arun V. Holden
David Lloyd
Lars F. Olsen
v
CONTENTS
Chaos in Physiology: Health or Disease?
A.L. Goldberger and B.J. West
Patterns of Activity in a Reduced Ionic Model of a Cell from
the Rabbit Sinoatrial Node ...•..........................•• 5
M.R. Guevara, A.C.G. van Ginneken and H.J. Jongsma
Oscillatory Plant Transpiration: Problem of a Mathematically
Correct Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . • • 13
I. Gumowski
Bifurcations in a Model of the Platelet Regulatory System 19
J. Belair
Chaos in a System of Interacting Nephrons .....................•• 23
K.S. Jensen, N.~H. Holstein-Rathlou, P.P. Leyssec,
E. Mosekilde and D.R. Rasmussen
Polypeptide Hormones and Receptors: Participants in and
Products of a Two-parameter, Dissipative, Measure
Preserving, Smooth Dynamical System in Hydrophobic
Ma.ss Energy ••••••••••••••••••••••••••••••••••••••••••••••• 33
A.J. Handell
Interplay Between Two Periodic Enzyme Reactions as a Source
for Complex Oscillatory Behaviour ........................•• 49
0. Decroly
Dynamics of Controlled Metabolic Network and Cellular Behaviour 59
S. Sinha and R. Ramaswamy
Periodic Forcing of a Biochemical System with Multiple Modes
of Oscillatory Behaviour ................................•• 67
F. Moran and A. Goldbeter
Periodic Behaviour and Chaos in the Mechanism of Intercellular
Communication Governing Aggregation of Dictyostelium
Amoebae 79
A. Goldbeter and J.L. Martiel
Turbulent Morphogenesis of a Prototype Reaction-Diffusion
System . . . . . • . . . . . . . . • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • • 91
J. Parisi, B. Rohricht, J. Peinke and O.E. Rossler
vii
Periodic Solutions and Global Bifurcations for Nerve
Impulse Equations • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • 97
M. Rosirio L.M.S. Alvares-Ribeiro
Homoclinic and Periodic Solutions of Nerve Impulse Equations •••••• 105
I.S. Labouriau
High Sensitivity Chaotic Behaviour in Sinusoidally Driven
Hodgkin-Huxley Equations •••••••••••••.•••••••••••••••••••• 113
P. Arrigo, L. Marconi, G. Morgavi, S. Ridella, C. Rolando
and F. Scalia
Forced Oscillations and Routes to Chaos in the Hodgkin-Huxley
Axons and Squid Giant Axons •••••••••••••••••••••••• , • • • • • • 121
K. Aihara and G. Matsumoto
Quantification of Chaos from Periodically 'Forced
Squid Axons . . . . . . . • . . • • . • • . . . . . . . . . • . • . • . . . . . • . . . . . . . . . . . • . 133
R.M. Everson
Chaos, Phase Locking and Bifurcation in Normal Squid Axons 143
G. Matsumoto, N. Takahashi andY. Hanyu
Chaos in Molluscan Neuron ••••••••••••••••••••••••••••• , • • • • • • • • • • 157
H. Hayashi and S. Ishizuka
Pancreatic B-Cell Electrical Activity: Chaotic and Irregular
Bursting Pattern • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 167
P. Lebrun
Multiple Oscillatory States and Chaos in the Endogenous
Activity of Excitable Cells: Pancreatic B-Cell as
an Example ••••••••••••••••••••••••••••••.•••.••••••• , • • • • • 173
T.R. Chay and H.S. Kang
Bifurcations in the Rose-Hindmarch and the Chay Model 183
C. Kaas-Petersen
Dendritic Branching Patterns 191
A.K. Schierwagen
Chaos and Neural Networks 195
•••••••••••••••••••••••••••• Ill •••••••••••
E. Labos
Data Requirements for Reliable Estimation of Correla~ion
DimensiotlS .......•..........•.....•........ , , , , ..... 207
111 ..... ,
A.M. Albano, A.I. Mees, G.C. de Guzman and P.E. Rapp
Chaotic Dynamics in Biological Information Processing:
A Heuristic Outline •••••••••••••••••••••••••• , • • • • • • • • • • • • 221
J.S. Nicholis
Chaos in Ecology and Epidemiology 233
e I I e I I • e I e I I I I I II I II II I I I II I ' I ' • ' II II
W.M. Schaffer
Low Dimensional Storage Attractors in Epidemics of Childhood
Diseases in Copenhagen, Denmark ••••.•••••••••••••••••••••• 249
L.F. Olsen
viii
Periodicity and Chaos in Biological Systems: New Tools for
the Study of Attractors •••.•..•.••.••..••..•..••..•.••.• 255
J. Demongeot, C. Jacob and P. Cinquin
Populations Under Periodically and Randomly Varying Growth
Conditions • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • . . . • . . • • . • • . • • 267
M. Markus, B. Hess, J. RBssler and M. Kiwi
Bi-fractal Basin Boundaries in Invertible Systems 279
O.E. Rossler, C. Kahlert and J.L. Hudson
Homoclinic Bifurcations in Ordinary Differential Equations 285
P. Glendinning
Characterization of Order and Disorder in Spatial Patterns 295
M. Markus, S.C. MUller, T. Plesser and B. Hess
Fractals, Intermittency and Morphogenesis 305
B.J. West
Temperature Stability of Davydov Solitons ••••••••••.••••••••.• 315
L. Cruzeiro, P.L. Christiansen, J. Halding, 0. Skovgaard
and A.C. Scott
Index 321
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