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 `index.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 f2clibs.tar.Z or just pick up the binary for your computer and the documentation, xpp_doc.ps.Z

# 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.

##
  I. Introduction

  ###

  A. Discrete Systems

  B. Continuous Systems

  II. Creating and running an ODE file.

  ###

  Quitting and aborting a calculation

  Integrating the equations

  Change parameters

  Graphics tricks

  Examining the numbers

  Fixed points and stability

  Homework 1.1
  Homework 1.2
  III. Nonlinear ODES

  ###

  Adding a nonlinear conductance
  User defined functions
  Auxiliary quantities
  Homework 1.3
  Fixed quantities
  Homework 1.4
  Multiple equilibria
  The numerics menu explored
  Creating another window
  Homework 1.5
  AUTO the first run through
  Two-parameter curves and cusps
  Homework 1.6

  IV. Two dimensional systems

  ###

  The Reduced Morris-Lecar Equations
  More Plotting Tricks

  #### Homework 2.1

  Phase plane analysis
  Nullclines
  Homework 2.2
  Three-d windows and Kinescope
  Hopf bifurcation
  Limit cycles
  AUTO again
  Bistability
  Saddle-point excitability
  Separatrix
  More AUTO

  V. Beyond Two dimensions

  ###

  Chaos, period doubling, Poincare maps
  A simple three-dimesnional system
  Hopf bifurcation and period doubling
  Chaos
  Creating a Poincare map
  Approximation of the return map by a discrete dynamical system
  Weak coupling of oscillators
  Morris-Lecar with synapses
  Computing interaction functions
  Getting Fourier approximations

# References

##

  Main Menu Items
  Numerics Menu
  Freeze Menu
  I/O and Hardcopy
  Nonlinear ODEs
  Three-dimensions and Beyond
  Chaos