A Dynamical Systems Package Running Under Mathematica
Updated May 30, 2013
Trapping a Limit Cycle
From the Application OrbitTrap.nb
Description of Package
This package contains routines for integrating and plotting solutions of systems of nonlinear ordinary differential equations. The package runs under Mathematica. The Mathematica code in the package is fully documented. There are 21 tutorial notebooks to give you a quick introduction to various features of DynPac. The titles of those tutorials give a brief summary of the scope of the package: Introduction to DynPac; Integration and Plotting (2D); Integration and Plotting (3D); Equilibrium and Stability; Local Solution Near Equilibrium Point; Comparison of Integration Methods; Periodic Solutions of Autonomous Systems; Periodic Solutions of Driven Systems; Orbit Trapping and Index Theory; Phase Portraits; Bifurcation Sequences; Liapunov Functions; Coloring, Dashing and Filling; The Lorenz Equations; Animating the Lorenz Attractor; Graph Labels; Lag Equations; Iterated Maps; A Single First-Order Equation; Transformations of Systems; Choosing a Time Step. A number of sample applications are included in addition to these tutorials.
The files available below for downloading are all in the form of Mathematica notebooks, and should work in Mac OS X, Windows, or Unix. They are available here in zip compression. If you need another form of compression, let me know and I will email the compressed files to you.
Downloading a Movie Demo
A four minute movie demo may be downloaded below. The movie shows 10 short film clips, created with DynPac, of various dynamical systems. The movie is a self-contained Quicktime movie and does not require DynPac to run. It is available in uncompressed form or in zip compression.
Movie Demo (uncompressed 11.3 M)
Movie Demo in zip compression (4.3 M)
DynPac for Mathematica 5
The most recent and also the final version of DynPac for Mathematica 5 is 10.72 (dated June 23, 2008).
DynPac 10.72 for Mathematica 5 in zip compression
DynPac for Mathematica 6
The most recent version of DynPac for Mathematica 6 is 11.02 (dated February 25, 2009). There were hundreds of changes required to get the code for Mathematica 5 to run in Mathematica 6, so the likelihood of bugs remaining is higher than I would like. I no longer have access to Mathematica 5 or 6, so I am unable to do any major repairs to DynPac 10.72 or 11.02.
DynPac 11.02 for Mathematica 6 in zip compression
DynPac for Mathematica 7
Essentially no changes were required to get DynPac for Mathematica 6 to run in Mathematica 7, although a few very small bugs and errors were corrected. Version 11.03 has been extensively tested in Mathematica 7. I have also tested it in Mathematica 8, and, to the best of my knowledge it will run in Mathematica 8.
DynPac 11.03 for Mathematica 7 in zip compression
DynPac for Mathematica 8
DynPac 11.04 has been thoroughly tested in Mathematica 8. It differs from version 11.03 in making more use of Manipulate panels for graph sequences. Although I have not tested it extensively in Mathematica 7, it does seem to run in 7, and would probably be a better choice than 11.03 because of the increased functionality for graph sequences.
DynPac 11.04 for Mathematica 8 in zip compression
DynPac for Mathematica 9
I have tested DynPac 11.04 in Mathematica 9 and it seems to run with no problems. I plan to do more thorough testing this summer, and I hope to add more functions taking advantage of dynamic variables and Manipulate.
Dept. of Mechanical Engineering
University of Rochester
Rochester, NY 14627
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