Dynamics of biological systems

Michael Small

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(R) implementations of algorithms and case studies are available on the author's website.

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[目次]

  • 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.

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この本の情報

書名 Dynamics of biological systems
著作者等 Small, Michael, Dr.
Small Michael
シリーズ名 Chapman and Hall/CRC mathematical & computational biology series
出版元 CRC Press/Taylor & Francis
刊行年月 c2012
ページ数 xv, 262 p.
大きさ 25 cm
ISBN 9781439853368
NCID BB11914428
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言語 英語
出版国 アメリカ合衆国
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