Analysis of Dynamical Systems

For our class "Complex Analysis" we decided to build a program that would allow the user to specify functions and curves and graph them under iteration in order to study their dynamics. Originally, this program allowed the user to specify four dynamical systems (functions) and up to six "curves of initial conditions". Any of the curves could then be applied to the functions. Finally the user could specify how many times to iterate the functions. This would allow the results of the graphing to be as simple or complicated as the user wanted.

With the help of a Wilson Scholorship, we decided to continue the project into the next school year. Many updates have already been made. One of these updates allows the user to specify a range of iterations. This gives the user more control over what he/she sees after each graphing. Another update includes the ability to color the graphed lines based upon each combination of curves and functions.



Future updates to this program include a parser to allow the user to declare variables, a zoom feature to quickly adjust the view coordinates, and the ability to graph the trajectory of a given initial condition on top of an existing graph. After these updates have been made, we plan on putting our program to work by using it to study examples of dynamical systems from Dr. Daniel Jackson's Ph.D. thesis. After the development of the program and our research has conluded, we will release our results during the 2008 UMF Symposium Day.

To try this program, please vist http://students.umf.maine.edu/~basselhn/.