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TitleNonlinear Dynamics in Physiology and Medicine [electronic resource] / edited by Anne Beuter, Leon Glass, Michael C. Mackey, Michรจle S. Titcombe
ImprintNew York, NY : Springer New York : Imprint: Springer, 2003
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Descript XXVI, 436 p. online resource


This book deals with the application of mathematics in modeling and understanding physiological systems, especially those involving rhythms. It is divided roughly into two sections. In the first part of the book, the authors introduce ideas and techniques from nonlinear dynamics that are relevant to the analysis of biological rhythms. The second part consists of five in-depth case studies in which the authors use the theoretical tools developed earlier to investigate a number of physiological processes: the dynamics of excitable nerve and cardiac tissue, resetting and entrainment of biological oscillators, the effects of noise and time delay on the pupil light reflex, pathologies associated with blood cell replication, and Parkinsonian tremor. One novel feature of the book is the inclusion of classroom-tested computer exercises throughout, designed to form a bridge between the mathematical theory and physiological experiments. This book will be of interest to students and researchers in the natural and physical sciences wanting to learn about the complexities and subtleties of physiological systems from a mathematical perspective. The authors are members of the Centre for Nonlinear Dynamics in Physiology and Medicine. The material in this book was developed for use in courses and was presented in three Summer Schools run by the authors in Montreal


1 Theoretical Approaches in Physiology -- 2 Introduction to Dynamics in Nonlinear Difference and Differential Equations -- 3 Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems -- 4 Dynamics of Excitable Cells -- 5 Resetting and Entraining Biological Rhythms -- 6 Effects of Noise on Nonlinear Dynamics -- 7 Reentry in Excitable Media -- 8 Cell Replication and Control -- 9 Pupil Light Reflex: Delays and Oscillations -- 10 Data Analysis and Mathematical Modeling of Human Tremor -- A An Introduction to XPP -- Michael C. Mackey -- A.1 ODE Files -- A.2 Starting and Quitting XPP -- A.3 Time Series -- A.4 Numerics -- A.5 Graphic Tricks -- A.5.1 Axis -- A.5.2 Multiplotting -- A.5.3 Erasing -- A.5.4 Printing the Figures -- A.6 Examining the Numbers -- A.7 Changing the Initial Condition -- A.8 Finding the Fixed Points and Their Stability -- A.9 Drawing Nullclines and Direction Field -- A.10 Changing the Parameters -- A.11 Auto -- A.11.1 Bifurcation Diagram -- A.11.2 Scrolling Through the Points on the Bifurcation Diagram -- A.12 Saving Auto Diagrams -- B An Introduction to Matlab -- Michรจle S. Titcombe and Caroline Haurie -- R.1 Starting and Quitting Matlab -- B.2 Vectors and Matrices -- B 2 1 Creating Matrices and Vectors -- .B.3 Suppressing Output to the Screen (the Semicolon!) -- B.4 Operations on Matrices -- B.5 Programs (M-Files) -- B.5.1 Script Files -- B.5.2 Function Files -- B.6 The Help Command -- B.7 Loops -- B.8 Plotting -- B.8.1 Examples -- B.8.2 Clearing Figures and Opening New Figures -- B.8.3 Symbols and Colors for Lines and Points -- B.9 Loading Data -- B.9.1 Examples -- B.10 Saving Your Work -- C Time Series Analysis -- Roderick Edwards and Michรจle S. Titcombe -- C.1 The Distribution of Data Points -- C.2 Linear Processes -- C.3 Fourier Analysis

Mathematics Neurosciences Neurobiology Biomathematics Biophysics Biological physics Mathematics Mathematical and Computational Biology Neurosciences Neurobiology Biophysics and Biological Physics


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