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Nonlinear Dynamics in Physiology and Medicine

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...

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Bibliographic Details
Other Authors: Beuter, Anne (Editor), Glass, Leon (Editor), Mackey, Michael C. (Editor), Titcombe, Michele S. (Editor)
Format: eBook
Language:English
Published: New York, NY Springer New York 2003, 2003
Edition:1st ed. 2003
Series:Interdisciplinary Applied Mathematics
Subjects:
Neuroscience
Neurosciences
Mathematical And Computational Biology
Biomathematics
Biophysics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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

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