Nonlinear Dynamics in Physiology and Medicine

2003
ISBN: 978-0-387-00449-5
Verlag: Springer

Buch, Englisch, Band 25, 436 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1830 g

Reihe: Interdisciplinary Applied Mathematics

Je tiens impossible de connaître les parties sans connaître le tout, non plus que de connaître le tout sans connaître particulierement les parties -Pascal The eterna[ mystery of the world is its comprehensibility -Einstein This book deals with the application of mathematical tools to the study of physiological systems. It is directed toward an audience of physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathemati­ cians, and others interested in finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical per­ spective. We have attempted to give a broad view of the underlying notions behind the dynamics of physiological rhythms, sometimes from a theoretical perspective and sometimes from the perspective of the experimentalist. This book can be used in a variety of ways, ranging from a more tra­ ditional approach such as a textbook in a biomathematics course (at either the advanced undergraduate or graduatelevel) to a research re­ source in which someone interested in a particular problem might look at the corresponding discussion here to guide their own thinking. We hope that researchers at all levels will find inspiration from the way we have dealt with particular research problems to tackle completely new areas of investigation, or even approach these in totally new ways.

Zielgruppe

Graduate

Autoren/Hrsg.

Beuter, Anne

Titcombe, Michele S.

Glass, Leon

Mackey, Michael C.

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
• Naturwissenschaften Biowissenschaften Biowissenschaften Neurobiologie, Verhaltensbiologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Klinische und Innere Medizin Neurologie, Klinische Neurowissenschaft
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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 theBifurcation Diagram.- A.12 Saving Auto Diagrams.- B An Introduction to Matlab.- Michèle 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 Michèle S. Titcombe.- C.1 The Distribution of Data Points.- C.2 Linear Processes.- C.3 Fourier Analysis.