Ebook: Chaos in Biological Systems

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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Content:
Front Matter....Pages i-xi
Chaos in Physiology: Health or Disease?....Pages 1-4
Patterns of Activity in a Reduced Ionic Model of a Cell from the Rabbit Sinoatrial Node....Pages 5-12
Oscillatory Plant Transpiration: Problem of a Mathematically Correct Model....Pages 13-18
Bifurcations in a Model of the Platelet Regulatory System....Pages 19-22
Chaos in a System of Interacting Nephrons....Pages 23-32
Polypeptide Hormones and Receptors: Participants in and Products of a Two Parameter, Dissipative, Measure Preserving, Smooth Dynamical System in Hydrophobic Mass Energy....Pages 33-48
Interplay between Two Periodic Enzyme Reactions as a Source for Complex Oscillatory Behaviour....Pages 49-58
Dynamics of Controlled Metabolic Network and Cellular Behaviour....Pages 59-66
Periodic Forcing of a Biochemical System with Multiple Modes of Oscillatory Behaviour....Pages 67-77
Periodic Behaviour and Chaos in the Mechanism of Intercellular Communication Governing Aggregation of Dictyostelium Amoebae....Pages 79-89
Turbulent Morphogenesis of a Prototype Model Reaction-Diffusion System....Pages 91-95
Periodic Solutions and Global Bifurcations for Nerve Impulse Equations....Pages 97-104
Homoclinic and Periodic Solutions of Nerve Impulse Equations....Pages 105-111
High Sensitivity Chaotic Behaviour in Sinusoidally Driven Hodgkin-Huxley Equations....Pages 113-119
Forced Oscillations and Routes to Chaos in the Hodgkin-Huxley Axons and Squid Giant Axons....Pages 121-131
Quantification of Chaos from Periodically Forced Squid Axons....Pages 133-142
Chaos, Phase Locking and Bifurcation in Normal Squid Axons....Pages 143-156
Chaos in Molluscan Neuron....Pages 157-166
Pancreatic B-Cell Electrical Activity: Chaotic and Irregular Bursting Pattern....Pages 167-171
Multiple Oscillatory States and Chaos in the Endogenous Activity of Excitable Cells: Pancreatic ?-Cell as an Example....Pages 173-181
Bifurcations in the Rose-Hindmarch Model and the Chay Model....Pages 183-190
Dendritic Branching Patterns....Pages 191-193
Chaos and Neural Networks....Pages 195-206
Data Requirements for Reliable Estimation of Correlation Dimensions....Pages 207-220
Chaotic Dynamics in Biological Information Processing: A Heuristic Outline....Pages 221-232
Chaos in Ecology and Epidemiology....Pages 233-248
Low Dimensional Strange Attractors in Epidemics of Childhood Diseases in Copenhagen, Denmark....Pages 249-254
Periodicity and Chaos in Biological Systems: New Tools for the Study of Attractors....Pages 255-265
Populations under Periodically and Randomly Varying Growth Conditions....Pages 267-277
Bi-Fractal Basin Boundaries in Invertible Systems....Pages 279-283
Homoclinic Bifurcations in Ordinary Differential Equations....Pages 285-293
Characterization of Order and Disorder in Spatial Patterns....Pages 295-303
Fractals, Intermittency and Morphogenesis....Pages 305-314
Temperature Stability of Davydov Solitons....Pages 315-319
Back Matter....Pages 321-323

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Content:
Front Matter....Pages i-xi
Chaos in Physiology: Health or Disease?....Pages 1-4
Patterns of Activity in a Reduced Ionic Model of a Cell from the Rabbit Sinoatrial Node....Pages 5-12
Oscillatory Plant Transpiration: Problem of a Mathematically Correct Model....Pages 13-18
Bifurcations in a Model of the Platelet Regulatory System....Pages 19-22
Chaos in a System of Interacting Nephrons....Pages 23-32
Polypeptide Hormones and Receptors: Participants in and Products of a Two Parameter, Dissipative, Measure Preserving, Smooth Dynamical System in Hydrophobic Mass Energy....Pages 33-48
Interplay between Two Periodic Enzyme Reactions as a Source for Complex Oscillatory Behaviour....Pages 49-58
Dynamics of Controlled Metabolic Network and Cellular Behaviour....Pages 59-66
Periodic Forcing of a Biochemical System with Multiple Modes of Oscillatory Behaviour....Pages 67-77
Periodic Behaviour and Chaos in the Mechanism of Intercellular Communication Governing Aggregation of Dictyostelium Amoebae....Pages 79-89
Turbulent Morphogenesis of a Prototype Model Reaction-Diffusion System....Pages 91-95
Periodic Solutions and Global Bifurcations for Nerve Impulse Equations....Pages 97-104
Homoclinic and Periodic Solutions of Nerve Impulse Equations....Pages 105-111
High Sensitivity Chaotic Behaviour in Sinusoidally Driven Hodgkin-Huxley Equations....Pages 113-119
Forced Oscillations and Routes to Chaos in the Hodgkin-Huxley Axons and Squid Giant Axons....Pages 121-131
Quantification of Chaos from Periodically Forced Squid Axons....Pages 133-142
Chaos, Phase Locking and Bifurcation in Normal Squid Axons....Pages 143-156
Chaos in Molluscan Neuron....Pages 157-166
Pancreatic B-Cell Electrical Activity: Chaotic and Irregular Bursting Pattern....Pages 167-171
Multiple Oscillatory States and Chaos in the Endogenous Activity of Excitable Cells: Pancreatic ?-Cell as an Example....Pages 173-181
Bifurcations in the Rose-Hindmarch Model and the Chay Model....Pages 183-190
Dendritic Branching Patterns....Pages 191-193
Chaos and Neural Networks....Pages 195-206
Data Requirements for Reliable Estimation of Correlation Dimensions....Pages 207-220
Chaotic Dynamics in Biological Information Processing: A Heuristic Outline....Pages 221-232
Chaos in Ecology and Epidemiology....Pages 233-248
Low Dimensional Strange Attractors in Epidemics of Childhood Diseases in Copenhagen, Denmark....Pages 249-254
Periodicity and Chaos in Biological Systems: New Tools for the Study of Attractors....Pages 255-265
Populations under Periodically and Randomly Varying Growth Conditions....Pages 267-277
Bi-Fractal Basin Boundaries in Invertible Systems....Pages 279-283
Homoclinic Bifurcations in Ordinary Differential Equations....Pages 285-293
Characterization of Order and Disorder in Spatial Patterns....Pages 295-303
Fractals, Intermittency and Morphogenesis....Pages 305-314
Temperature Stability of Davydov Solitons....Pages 315-319
Back Matter....Pages 321-323
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