Chaos and Time-Series Analysis

This page contains supplementary materials, computer software, color figures, animations, errata, and links to web resources for the text Chaos and Time-Series Analysis (Oxford University Press, 2003).  It is organized according to the chapters in the book:

Preface

• Home page for the author
• Home page of the course for which the book was written
• Errata
• Changes for next edition
• Solutions to exercises (incomplete - volunteer needed!)
  

Chapter 1: Introduction

• Introduction to Chaos and Time-Series Analysis
• Chaos Demonstrations software
• Biography of Jules Henri Poincare'
• Saturn's moon Hyperion
• Uncropped color version of Fig. 1.3
• Uncropped color version of Fig. 1.4
• Uncropped color version of Fig. 1.5
• Animated version of Fig. 1.6
• Uncropped color version of Fig. 1.7
• Uncropped color version of Fig. 1.8
• Uncropped color version of Fig. 1.9
• Uncropped color version of Fig. 1.10
• Uncropped color version of Fig. 1.14
• Uncropped color version of Fig. 1.17
• Chua's circuit

Chapter 2: One-dimensional maps

• One-Dimensional Maps
• Conjugacy in dynamical systems
• The period doubling route to chaos
• Feigenbaum constants (values)
• Feigenbaum accumulation point (value)
  
• Numerical errors in logistic map calculation
• Cantor set description
• Sarkovskii's theorem
• Random number generator
  

Chapter 3: Nonchaotic multidimensional flows

• Nonchaotic Multidimensional Flows
• A primer on differential equations
• Uncropped color version of Fig. 3.4
• Chaos in Euler solution of ODEs

Chapter 4: Dynamical systems theory

• Dynamical Systems Theory
• Animated version of Fig. 4.12
• Animated version of Fig. 4.13
• Animated version of Fig. 4.14
• Proof that the Lorenz system is chaotic
• Simplest dissipative chaotic flow
• Other simple chaotic flows
• Mathematical models of love and happiness

Chapter 5: Lyapunov exponents

• Lyapunov Exponents
• Biography of Aleksandr Mikhailovich Lyapunov
• Numerical calculation of largest Lyapunov exponent
• Lyapunov exponent and dimension of the Lorenz attractor
• Improved Kaplan-Yorke dimension
• Wolf Lyapunov exponent software
• Hyperchaos
  

Chapter 6: Strange attractors

• Strange Attractors
• Strange Attractors: Creating Patterns in Chaos
• Stilson's 3-D strange attractors
• Stretching and folding of a strange attractor
• Simple chaotic flow with ABS nonlinearity
• More simple chaotic flows with ABS nonlinearity
• Animated strange attractors
• 3-D Strange Attractor Rendering Software
  

Chapter 7: Bifurcations

• Bifurcations
• Homoclinic and heteroclinic orbit animations
• Basic bifurcation phenomena

Chapter 8: Hamiltonian chaos

• Hamiltonian Chaos
• A symmetric chaotic flow
• Original photo of Callie the cat
• Cat map
• Cat map (animated)

Chapter 9: Time-series properties

• Time-Series Properties
• Madison, WI temperature data
• Audible version of Fig. 9.7
• Animated Necker cube
• Gaussian white noise data
• Deterministic Gaussian white data
• Tübingen time-series analysis group
• Practical implementation of nonlinear time series methods

Chapter 10: Nonlinear prediction and noise reduction

• Nonlinear Prediction and Noise Reduction
• Introduction to cross recurrence plots
• Back-propagation neural networks
• A solution of exercise 10.22
  

Chapter 11: Fractals

• Fractals
• Sprott's fractal gallery
• Bibliography of fractal geometry and spatial phenomena
• Fractal software
• Fractal frequently asked questions (FAQ)
• Fractal clouds
• Infinite fractal loop
• Fractals: An introductory lesson
• An introduction to Lindenmayer systems
• Fractals in the biological sciences
• JAVA fractals by James Henstridge

Chapter 12: Fractal dimension

• Calculation of Fractal Dimension
• Measuring the fractal dimension of natural objects

Chapter 13: Fractal measure and multifractals

• Multifractals
• Improved correlation dimension calculation

Chapter 14: Nonchaotic fractal sets

• Other Fractal Sets
• Classic sets
• DNS sequence for molluscum contagiosum virus
• Search engine for genome data bases
• FRACTINT home page
• Mandelbrot set chaos
• Introduction to quaternions

Chapter 15: Spatiotemporal chaos and complexity

• Spatiotemporal Chaos and Complexity
• Artificial Life
• Self-organizating systems FAQ
• Complexity Digest
• Quantifying self-organization, especially in cellular automata

Appendices

• Chaos data generator
  
• Journals with chaos and related papers

Time-Series Analysis Software

• Auguri
  
• Benoit Fractal Analysis System
• Biosignal Analysis Software
  
• Chaos Data Analyzer
• Dataplore Software and Analysis (formerly SANTIS)
• FracLab Fractal Analysis Toolbox for Signal and Image Processing
• HRV Analysis Software
  
• LagSpace
  
• Physio Toolkit
• Software for Data Mining / Web Mining
• TISEAN Nonlinear Time Series Analysis
• Visual Recurrence Analysis
• WINGRAMM Grammar Complexity Program

General references

• Basic concepts in nonlinear dynamics and chaos
• Chaos: Classical and Quantum (Web book)
  
• Chaos and fractals (Thinkquest)
• Chaos hypertext book
• The chaos metalink
• Chaos on the Web
• Chaos under control
• Earliest use of some words of mathematics
• Eric Weisstein's world of mathematics
• General chaos and nonlinear dynamics references
• Introduction to fractals and chaos
• The MacTutor history of mathematics archive
• Order, on-line chaos course
• Publications of University of Maryland chaos group
• Sci.nonlinear frequently asked questions
• On-line Encyclopedia for Integer Sequences

Reviews

• Fred Abraham in Nonlinear Dynamics in Psychology and Life Sciences
• Jeff Scargle in Technometrics
• Customer reviews from Amazon.com
  

Look inside the book

• Using Amazon.com

Ordering information

• From the publisher (Oxford University Press)
  
• From Amazon.com
• From Barnes & Noble
• To request an inspection copy