Dynamics of Biological Systems

About this book

Applying complex systems science to biology, this book develops mathematical models for understanding biological systems. 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.

Contents

Biological Systems and Dynamics In the Beginning The Hemodynamic System Cheyne-Stokes Respiration Summary 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 Summary Observability of Dynamic Variables Bioelectric Phenomena Measurement ECG, EEG, EMG, EOG and All That Measuring Movement Measuring Temperature Measuring Oxygen Concentration Biomedical Imaging Foetal Heart Monitoring Real Time Development of Neuronal Connectivity The Importance of Measurement Summary Biomedical Signal Processing Segmentation Error Measure and Automatic Analysis of Electroencephalograms Electrocardiographic Signal Processing Vector Cardiography Embedology and State Space Representation Linear Signal Processing Data Processing Time Series Analysis Fractals, Chaos and Nonlinear Dynamics #Prediction Summary Computational Neurophysiology The Cell Action Potentials and Ion Channels Ficks Law, Ohms Law and the Einstein Relation Cellular Equilibrium: Nernst and Goldman Equivalent Circuits Summary Mathematical Neurodynamics Hodgkin, Huxley and the Squid Giant Axon Fitzhugh Nagumo Model Fixed Points and Stability of s Ode Dimensional Differential Equation Null Clines and Phase Plane Pitchfork and Hopf Bifurcations In Two Dimensions Bursting, Excitability and Exotic Bifurcations 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 Tiered Populations HIV/AIDS Summary Action, Reaction and Diffusion Black Death and Spatial Disease Transmission Reaction-Diffusion Cardiac Dynamics Pacemaker Cells, Synchronisation and Diffusion Summary Autonomous Agents Flocking Celluloid penguins and roosting starlings Crowd simulation Mexican waves, Mecca and fire escapes Summary Complex Networks Human Networks: Growing Complex Networks Global Spread of Avian Influenza Complex Disease Transmission and Immunisation Neuronal Networks in the Nematode Worm Growth of Connections among Neural Stem Cells and in the Developing Hippocampus Interaction of Grazing Herbivores Summary Potential and Limitations Models Reflect Reality What Pandemic? Predicting the Next Influenza Pandemic The Human Genome Models Have Limitations Interpolation and Extrapolation The Physiome Project Appendix A: Some More Mathematics Differential Equations Vector Calculus Partial Differential Equations Stochastic Methods Computational and Numerical Methods Appendix B: Solutions Appendix C: Teaching Material Lecture Slides MATLAB code Mathematica Demonstrations Sample Data

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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.