Dynamics of Biological Systems

ISBN-10: 1439853363
ISBN-13: 9781439853368
Edition: 2011
Authors: Michael Small
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Description: Applying complex systems science to biology, this book develops mathematical models for understanding biological systems. Based on his one-semester course, the author suggests appropriate control strategies to mediate the effects of past and future  More...

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Book details

List price: $57.99
Copyright year: 2011
Publisher: Taylor & Francis Group
Publication date: 8/25/2011
Binding: Hardcover
Pages: 284
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 1.144
Language: English

Applying complex systems science to biology, this book develops mathematical models for understanding biological systems. Based on his one-semester course, the author suggests appropriate control strategies to mediate the effects of past and future pandemics, assuming no prior knowledge of mathematics. Each chapter presents exercises with worked solutions as well as computational and research projects. Topics covered include pattern formation and flocking behavior, the interaction of autonomous agents, hierarchical and structured network topologies, epidemiology, biomedical signal processing, computational neurophysiology, and population dynamics. A solutions manual is available for qualifying instructors.

Preface
Biological Systems and Dynamics
In the Beginning
The Hemodynamic System
Cheyne-Stokes Respiration
Summary
Population Dynamics of a Single Species
Fibonacci, Malthus and Nicholson's Blowflies
Fixed Points and Stability of a One-Dimensional First-Order Difference Equation
The Cobweb Diagram
An Example: Prostate Cancer
Higher-Dimensional Maps
Period-Doubling Bifurcation in Infant Respiration
Summary
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
Summary
Biomedical Signal Processing
Automatic Analysis of Electroencephalograms
Electrocardiographic Signal Processing
Vector Cardiography
Embedology and State Space Representation
Fractals, Chaos and Non-Linear Dynamics
Prediction
Summary
Computational Neurophysiology
The Cell
Action Potentials and Ion Channels
Fick's Law, Ohm's Law and the Einstein Relation
Cellular Equilibrium: Nernst and Goldman
Equivalent Circuits
Dendrites
Summary
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-Planes
Pitchfork and Hopf Bifurcations in Two Dimensions
Excitability
Summary
Population Dynamics
Predator-Prey Interactions
Fixed Points and Stability of Two-Dimensional Differential Equations
Disease Models: SIS, SIR and SEIR
SARS in Hong Kong
Summary
Action, Reaction and Diffusion
Black Death and Spatial Disease Transmission
Reaction-Diffusion
Cardiac Dynamics
Summary
Autonomous Agents
Flocking
Celluloid Penguins and Roosting Starlings
Evaluating Crowd Simulations
Summary
Complex Networks
Human Networks: Growing Complex Networks
Small-World Networks and the 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 Are Complex Networks
Summary
Conclusion
Models Are a Reflection of Reality
Bibliography
Index

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