Small Dynamics of Biological Systems

1. Auflage 2011
ISBN: 978-1-4398-9706-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 284 Seiten

Reihe: Chapman & Hall/CRC Mathematical & Computational Biology

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.

Autoren/Hrsg.

Small, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biophysik
• Naturwissenschaften Physik Angewandte Physik Biophysik
• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär Naturwissenschaften, Technik, Medizin

Inhaltsverzeichnis

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.