Dynamics of Biological Systems  book cover
1st Edition

Dynamics of Biological Systems

ISBN 9781439853368
Published August 25, 2011 by Chapman and Hall/CRC
276 Pages 11 Color & 112 B/W Illustrations

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Book Description

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.

Table of Contents

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.

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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.