Here are some resources to get you started with numerical computations. Since everyone has different backgrounds, I have included various options:
Matlab is the computing language of choice for APPM 2360, so many of you will already have some experience with it. Here is a link to some examples of Matlab applications to dynamical systems:
Using a spreadsheet like Excel you can quickly iterate one dimensional maps, implement Euler's method to solve differential equations, etc. Although it is simple to start with, it becomes limited for more complicated simulations. Here are some links to examples:
Once you get used to the conventions and the way to output and plot data, C++ gives you speed and control over what the simulation is doing. Here is some sample code that you can modify to get you started. To run these programs in Mac or Unix/Linux, go to the directory where you saved them in a terminal, type "make filename.cpp" and then "./filename", where "filename" is the name of the program. You will then have a text file with the data on two columns. You can plot this using gnuplot or importing it to Matlab or Mathematica.
Here is a C++ tutorial and resource site.
Mathematica is very powerful once you get used to its commands. Here is a link to very nice tutorial on Mathematica and the Logistic Map from Richard G. Palmer (Physics Department, Duke University), and a package for dynamical systems.
This is the example I used for linear stability on August 28:
This is the example I used for the Logistic Map on September 11:
This is the example I used for the bifurcation diagram of the logistic map on September (I also used "1D maps" from Jim Meiss):
There are many programs and applets devoted exclusively to the study of dynamical systems. Here are some links:
