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
Prediction
Computational Neurophysiology
The Cell
Action Potentials and Ion Channels
Ficks Law, Ohms Law and the Einstein Relation
Cellular Equilibrium: Nernst and Goldman
Equivalent Circuits
Dendrites
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
Excitability
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
Reaction-Diffusion
Cardiac Dynamics
Autonomous Agents
Flocking
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
Conclusion
Models Are a Reflection of Reality
References
A Summary appears at the end of each chapter.
Biography
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.
