DynPac
A Dynamical Systems Package Running Under Mathematica
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 5 or 6. 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 in two formats: sitx for Mac OS X, and zip for Windows. 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. The movie is available in compressed sitx form for MacOS X, and in compressed zip form for Windows. For a longer download but more immediate access to the movie, choose the uncompressed movie demo.
Movie Demo (uncompressed 11.3 M)
Movie Demo for Mac OS X (sitx 2.8 M)
Movie Demo for Windows (zip 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 and Mac OS X (sitx)
DynPac 10.72 for Mathematica 5 and Windows (zip)
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. Even though I have tested the code on all 21 tutorials and on the 31 applications included with the package, the probability of bugs remaining is higher than I would like. Reports of bugs and problems would be greatly appreciated. This version will probably run in Mathematica 7 also, but it has not yet been thoroughly tested in version 7
DynPac 11.02 for Mathematica 6 and Mac OS X (sitx)
DynPac 11.02 for Mathematica 6 and Windows (zip)
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.
DynPac 11.03 for Mathematica 7 and Mac OS X (sitx)
DynPac 11.03 for Mathematica 7 and Windows (zip)
Al Clark
Dept. of Mechanical Engineering
University of Rochester
Rochester, NY 14627
(585) 275-4078