This book introduces concepts from nonlinear dynamics using an almost exclusively biological setting for motivation, and includes examples of how these concepts are used in experimental investigations of biological and physiological systems. One novel feature of the book is the inclusion of classroom-tested computer exercises. This book will appeal to students and researchers working in the natural and physical sciences wanting to learn about physiological systems from a mathematical perspective.

Includes supplementary material: sn.pub/extras

Inhalt
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.