This tutorial will show you how to create files and run XPP as well as give you a brief overview of dynamical systems.

## Technical Setup

In order to run this tutorial properly, you must alter your .mailcap and .mime.types files so that the viewer knows what to do with the XPP files that are used in the tutorial. If you already have these files in your home directory, just add the lines in the two files to your existing ones. You also must be able to run XPP on your local machine. The command to call XPP must be xpp (The default compiled version is xppaut thus, you should make a link to that called xpp or just change it's name. Or, just change the `xpp` in the `.mime.types` and `.mailcap` files to `xppaut` .)

Since this tutorial takes a long time to run you might want to try it locally rather than over the network. In that case, get the compressed tarred files put them in a directory, uncompress and untar them. Then load `start.html` into your viewer.

### How do I get XPP?

Just ftp the program from ftp.math.pitt.edu/pub/bardware and pick up xppaut1.x.tar.Z and (possibly) f2clibs.tar.Z or just pick up the binary for your computer.

## Comments?

# Table of Contents

It is usually best to go through the various sections in order, but you can jump to any heading by clicking on it.

##

  Technical notes and setup
  Introduction

  ###

  Discrete dynamics
  Continuous dynamics

  Creating and running an ODE file

  ###

  Quitting
  Basics
  Integrating equations
  Changing parameters
  Graphics tricks
  Changing initial conditions
  Examining the numbers
  Fixed points and stability

  ####

  Stability window
  Homework 1.1
  Homework 1.2
  Nonlinear ODEs

  ###

  User defined functions
  Auxiliary quantities

  ####

  Homework 1.3
  Fixed quantities

  ####

  Homework 1.4
  Multiple equilibria and hysteresis
  Numerics menu
  Creating another window

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  Homework 1.5
  AUTO for the first time
  Two parameter curves and the cusp

  ####

  Homework 1.6
  Two-dimensional systems

  ###

  ####

  More plotting tricks
  Homework 2.1
  Periodics and phase-plane analysis

  ###

  Nullclines
  Three-d windows and kinescope

  ####

  Homework 2.2
  The Hopf bifurcation theorem -- AUTO II

  ####

  Frequency information
  Homework 2.3
  Homework 2.4
  Beyond 2 dimensions

  ###

  Averaging and weakly coupled oscillators

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  Response and interaction functions
  Symmetric coupling
  Homework 3.1
  Homework 3.2
  Phase equations

  ###

  Poincare maps
  Invariant density
  The standard map
  Cobwebbing
  Discrete dynamics

  ####

  Homework 3.3
  Chaos

  ###

  The simplest chaotic ODE
  Period doubling cascades
  Three-d views
  Chaos at last

  ####

  Poincare Map II
  Liapunov exponents
  Homework 5.1

# References

##

  Table of Contents
  Main Menu Items
  ODE Files and Examples
  Numerics Menu
  File Menu
  Freeze Menu
  AUTO Menu
  I/O and Hardcopy
  XPP Basics
  Nonlinear ODEs
  Two-dimensions
  Three-dimensions and Beyond
  Phase Equations
  Chaos