Understanding Nonlinear Dynamics

1 Finite-Difference Equations.- 1.1 A Mythical Field.- 1.2 The Linear Finite-Difference Equation.- 1.3 Methods of Iteration.- 1.4 Nonlinear Finite-Difference Equations.- 1.5 Steady States and Their Stability.- 1.6 Cycles and Their Stability.- 1.7 Chaos.- 1.8 Quasiperiodicity.- 1 Chaos in Periodically Stimulated Heart Cells.- Sources and Notes.- Exercises.- Computer Projects.- 2 Boolean Networks and Cellular Automata.- 2.1 Elements and Networks.- 2.2 Boolean Variables, Functions, and Networks.- 2 A Lambda Bacteriophage Model.- 3 Locomotion in Salamanders.- 2.3 Boolean Functions and Biochemistry.- 2.4 Random Boolean Networks.- 2.5 Cellular Automata.- 4 Spiral Waves in Chemistry and Biology.- 2.6 Advanced Topic: Evolution and Computation.- Sources and Notes.- Exercises.- Computer Projects.- 3 Self-Similarity and Fractal Geometry.- 3.1 Describing a Tree.- 3.2 Fractals.- 3.3 Dimension.- 5 The Box-Counting Dimension.- 3.4 Statistical Self-Similarity.- 6 Self-Similarity in Time.- 3.5 Fractals and Dynamics.- 7 Random Walks and Lévy Walks.- 8 Fractal Growth.- Sources and Notes.- Exercises.- Computer Projects.- 4 One-Dimensional Differential Equations.- 4.1 Basic Definitions.- 4.2 Growth and Decay.- 9 Traffic on the Internet.- 10 Open Time Histograms in Patch Clamp Experiments.- 11 Gompertz Growth of Tumors.- 4.3 Multiple Fixed Points.- 4.4 Geometrical Analysis of One-Dimensional Nonlinear Ordinary Differential Equations.- 4.5 Algebraic Analysis of Fixed Points.- 4.6 Differential Equations versus Finite-Difference Equations.- 4.7 Differential Equations with Inputs.- 12 Heart Rate Response to Sinusoid Inputs.- 4.8 Advanced Topic: Time Delays and Chaos.- 13 Nicholson's Blowflies.- Sources and Notes.- Exercises.- Computer Projects.- 5 Two-Dimensional Differential Equations.- 5.1 The Harmonic Oscillator.- 5.2 Solutions, Trajectories, and Flows.- 5.3 The Two-Dimensional Linear Ordinary Differential Equation.- 5.4 Coupled First-Order Linear Equations.- 14 Metastasis of Malignant

ANot only are many of the most recent topics included and simply explained, but the reader is also warned against difficulties in the practical implementation of the proposed methods of analysis and against common misinterpretations of some theoretical concepts. Because of its completeness and plain, but mathematically correct, style, this book is also an ideal starting point for researchers from various disciplines who are not familiar with mathematical concepts usually learned in the first two years of university study.A AMATHEMATICAL REVIEWS AI recommend this book strongly both to those who need to teach these topics and to those who want to learn about them, whether or not they are in the biosciences. In fact, I would strongly recommend this book to paleontologists, paleobiologists, paleoecologists, and geologists who are (finally) becoming interested in nonlinear dynamics, but are still afraid to ask.AAAMERICAN SCIENTIST A[The authors] have written a readily accessible introduction to nonlinear dynamicsAthe book presents the main concepts and applications of nonlinear dynamics at an elementary levelAInterspersed in the text are delightful short essays of a page or two eachACourses on nonlinear dynamics rarely present these topics at the level used in the bookAIt is written in a Auser friendlyA colloquial style and is a delight to readAno reader is likely to encounter a more accessible elementary introduction to nonlinear dynamics.AAPHYSICS TODAY