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.

Inhalt

Chaos in Physiology: Health or Disease?.- Patterns of Activity in a Reduced Ionic Model of a Cell from the Rabbit Sinoatrial Node.- Oscillatory Plant Transpiration: Problem of a Mathematically Correct Model.- Bifurcations in a Model of the Platelet Regulatory System.- Chaos in a System of Interacting Nephrons.- Polypeptide Hormones and Receptors: Participants in and Products of a Two-parameter, Dissipative, Measure Preserving, Smooth Dynamical System in Hydrophobic Mass Energy.- Interplay Between Two Periodic Enzyme Reactions as a Source for Complex Oscillatory Behaviour.- Dynamics of Controlled Metabolic Network and Cellular Behaviour.- Periodic Forcing of a Biochemical System with Multiple Modes of Oscillatory Behaviour.- Periodic Behaviour and Chaos in the Mechanism of Intercellular Communication Governing Aggregation of Dictyostelium Amoebae.- Turbulent Morphogenesis of a Prototype Reaction-Diffusion System.- Periodic Solutions and Global Bifurcations for Nerve Impulse Equations.- Homoclinic and Periodic Solutions of Nerve Impulse Equations.- High Sensitivity Chaotic Behaviour in Sinusoidally Driven Hodgkin-Huxley Equations.- Forced Oscillations and Routes to Chaos in the Hodgkin-Huxley Axons and Squid Giant Axons.- Quantification of Chaos from Periodically Forced Squid Axons.- Chaos, Phase Locking and Bifurcation in Normal Squid Axons.- Chaos in Molluscan Neuron.- Pancreatic B-Cell Electrical Activity: Chaotic and Irregular Bursting Pattern.- Multiple Oscillatory States and Chaos in the Endogenous Activity of Excitable Cells: Pancreatic B-Cell as an Example.- Bifurcations in the Rose-Hindmarch and the Chay Model.- Dendritic Branching Patterns.- Chaos and Neural Networks.- Data Requirements for Reliable Estimation of Correlation Dimensions.- Chaotic Dynamics in Biological Information Processing: A Heuristic Outline.- Chaos in Ecology and Epidemiology.- Low Dimensional Storage Attractors in Epidemics of Childhood Diseases in Copenhagen, Denmark.- Periodicity and Chaos in Biological Systems: New Tools for the Study of Attractors.- Populations Under Periodically and Randomly Varying Growth Conditions.- Bi-fractal Basin Boundaries in Invertible Systems.- Homoclinic Bifurcations in Ordinary Differential Equations.- Characterization of Order and Disorder in Spatial Patterns.- Fractals, Intermittency and Morphogenesis.- Temperature Stability of Davydov Solitons.