Dynamics of Biological Systems: 1st Edition (Hardback) book cover

Dynamics of Biological Systems

1st Edition

By Michael Small

Chapman and Hall/CRC

284 pages | 11 Color Illus. | 112 B/W Illus.

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pub: 2011-08-25
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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

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.

About the Author

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.

About the Series

Chapman & Hall/CRC Mathematical and Computational Biology

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MED009000
MEDICAL / Biotechnology
SCI055000
SCIENCE / Physics