1st Edition

Dynamics of Biological Systems

By Michael Small Copyright 2012
    276 Pages 11 Color & 112 B/W Illustrations
    by Chapman & Hall

    From the spontaneous rapid firing of cortical neurons to the spatial diffusion of disease epidemics, biological systems exhibit rich dynamic behaviour over a vast range of time and space scales. Unifying many of these diverse phenomena, Dynamics of Biological Systems provides the computational and mathematical platform from which to understand the underlying processes of the phenomena.

    Through an extensive tour of various biological systems, the text introduces computational methods for simulating spatial diffusion processes in excitable media, such as the human heart, as well as mathematical tools for dealing with systems of nonlinear ordinary and partial differential equations, such as neuronal activation and disease diffusion. The mathematical models and computer simulations offer insight into the dynamics of temporal and spatial biological systems, including cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behaviour, the interaction of autonomous agents, and hierarchical and structured network topologies. Tools from complex systems and complex networks are also presented for dealing with real phenomenological systems.

    With exercises and projects in each chapter, this classroom-tested text shows students how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. MATLAB® implementations of algorithms and case studies are available on the author’s website.

    Biological Systems and Dynamics
    In the Beginning
    The Hemodynamic System
    Cheyne-Stokes Respiration

    Population Dynamics of a Single Species
    Fibonacci, Malthus and Nicholsons Blowflies
    Fixed Points and Stability of a One-Dimensional First Order Difference Equation
    The Cobweb Diagram
    An Example: Hormone Secretion
    Higher Dimensional Maps
    Period Doubling Bifurcation in Infant Respiration

    Observability of Dynamic Variables
    Bioelectric Phenomena Measurement
    ECG, EEG, EMG, EOG and All That
    Measuring Movement
    Measuring Temperature
    Measuring Oxygen Concentration
    Biomedical Imaging
    The Importance of Measurement

    Biomedical Signal Processing
    Segmentation Error Measure and Automatic Analysis of EEGs
    ECG Signal Processing
    Vector Cardiography
    Embedology and State Space Representation
    Fractals, Chaos and Nonlinear Dynamics

    Computational Neurophysiology
    The Cell
    Action Potentials and Ion Channels
    Ficks Law, Ohms Law and the Einstein Relation
    Cellular Equilibrium: Nernst and Goldman
    Equivalent Circuits

    Mathematical Neurodynamics
    Hodgkin, Huxley and the Squid Giant Axon
    FitzHugh-Nagumo Model
    Fixed Points and Stability of a One-Dimensional Differential Equation
    Nullclines and Phase Plane
    Pitchfork and Hopf Bifurcations in Two Dimensions

    Population Dynamics
    Predator-Prey Interactions
    Fixed Points and Stability of Two-Dimensional Differential Equations
    Disease Models: SIS, SIR and SEIR
    SARS in Hong Kong

    Action, Reaction and Diffusion
    Black Death and Spatial Disease Transmission
    Cardiac Dynamics

    Autonomous Agents
    Celluloid Penguins and Roosting Starlings
    Evaluating Crowd Simulations

    Complex Networks
    Human Networks: Growing Complex Networks
    Small World Networks of Spread of SARS
    Global Spread of Avian Influenza
    Complex Disease Transmission and Immunisation
    Complex Networks Constructed from Musical Composition
    Interaction of Grazing Herbivores
    Neuronal Networks and Complex Networks

    Models Are a Reflection of Reality


    A Summary appears at the end of each chapter.


    Michael Small is a professor of mathematical modelling and director of the Phenomics and Bioinformatics Research Centre in the School of Mathematics and Statistics at the University of South Australia (as of October 2011). He was previously an associate professor in the Department of Electronic and Information Engineering at Hong Kong Polytechnic University. His research interests include nonlinear time series, chaos, and complex systems.