Chaos in Biological Systems

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Hans Degn, Arunn V. Holden, Lars Folke Olsen
Springer Science & Business Media, Oct 31, 1987 - Science - 326 pages
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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.
 

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Contents

HEALTH OR DISEASE?
1
PATTERNS OF ACTIVITY IN A REDUCED IONIC MODEL OF A CELL FROM THE RABBIT SINOATRIAL NODE
5
PROBLEM OF A MATHEMATICALLY CORRECT MODEL
13
BIFURCATIONS IN A MODEL OF THE PLATELET REGULATORY SYSTEM
19
CHAOS IN A SYSTEM OF INTERACTING NEPHRONS
23
PARTICIPANTS IN AND PRODUCTS OF A TWO PARAMETER DISSIPATIVE MEASURE PRESERVING SMOOTH DYNAMICAL SYSTEM IN ...
33
INTERPLAY BETWEEN TWO PERIODIC ENZYME REACTIONS AS A SOURCE FOR COMPLEX OSCILLATORY BEHAVIOUR
49
DYNAMICS OF CONTROLLED METABOLIC NETWORK AND CELLULAR BEHAVIOUR
59
CHAOTIC AND IRREGULAR BURSTING PATTERN
167
PANCREATIC BCELL AS AN EXAMPLE
173
BIFURCATIONS IN THE ROSEHINDMARCH MODEL AND THE CHAY MODEL
183
DENDRITIC BRANCHING PATTERNS
191
CHAOS AND NEURAL NETWORKS
195
DATA REQUIREMENTS FOR RELIABLE ESTIMATION OF CORRELATION DIMENSIONS
207
A HEURISTIC OUTLINE
221
CHAOS IN ECOLOGY AND EPIDEMIOLOGY
233

PERIODIC FORCING OF A BIOCHEMICAL SYSTEM WITH MULTIPLE MODES OF OSCILLATORY BEHAVIOUR
67
PERIODIC BEHAVIOUR AND CHAOS IN THE MECHANISM OF INTERCELLULAR COMMUNICATION GOVERNING AGGREGATION OF D...
79
TURBULENT MORPHOGENESIS OF A PROTOTYPE MODEL REACTIONDIFFUSION SYSTEM
91
PERIODIC SOLUTIONS AND GLOBAL BIFURCATIONS FOR NERVE IMPULSE EQUATIONS
97
HOMOCLINIC AND PERIODIC SOLUTIONS OF NERVE IMPULSE EQUATIONS
105
HIGH SENSITIVITY CHAOTIC BEHAVIOUR IN SINUSOIDALLY DRIVEN HODGKINHUXLEY EQUATIONS
113
FORCED OSCILLATIONS AND ROUTES TO CHAOS IN THE HODGKINHUXLEY AXONS AND SQUID GIANT AXONS
121
QUANTIFICATION OF CHAOS FROM PERIODICALLY FORCED SQUID AXONS
133
CHAOS PHASE LOCKING AND BIFURCATION IN NORMAL SQUID AXONS
143
CHAOS IN MOLLUSCAN NEURON
157
LOW DIMENSIONAL STRANGE ATTRACTORS IN EPIDEMICS OF CHILDHOOD DISEASES IN COPENHAGEN DENMARK
249
NEW TOOLS FOR THE STUDY OF ATTRACTORS
255
POPULATIONS UNDER PERIODICALLY AND RANDOMLY VARYING GROWTH CONDITIONS
267
BIFRACTAL BASIN BOUNDARIES IN INVERTIBLE SYSTEMS
279
HOMOCLINIC BIFURCATIONS IN ORDINARY DIFFERENTIAL EQUATIONS
285
CHARACTERIZATION OF ORDER AND DISORDER IN SPATIAL PATTERNS
295
FRACTALS INTERMITTENCY AND MORPHOGENESIS
305
TEMPERATURE STABILITY OF DAVYDOV SOLITONS
315
INDEX
321
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