Great Software for Dynamical Systems
For a overview of the subject, see Wikipedia: Dynamical systems.
For a text book, see my friend Professor Palais's book at http://ode-math.com/
There is a Non-liner science FAQ at http://amath.colorado.edu/faculty/jdm/faq.html . Editor is James D Meiss.
★ StdMap. Standard Maps displays the dynamics of several area preserving mappings. It will also find periodic orbits, cantori, and stable and unstable manifolds of any (symmetric) periodic orbit.
The program is written by mathematician J D Meiss. Home page at: http://amath.colorado.edu/faculty/jdm/programs.html OSX
1DMap is another program by mathematician J D Meiss. It plots orbit maps of various equations, including: logistic, cosine, cubic, exp, tangent, tent, circle. For each, one can plot the correspondig cobweb, bifurcation diagram, and other statstical diagrams. The program is intuitive, but there is no documentation or tutorial, so the reader must already be familiar with the mathematics. Some text books on 1D dynamic systems are suggested on his website.
Home page at: http://amath.colorado.edu/faculty/jdm/1DMaps.html OSX
Cycle Explorer (screenshot) is a simple program that draws orbit maps of the equation f[x]:=x^2+c. Author is Jim Burgess.
home page at http://www.efn.org/~jcburg/software.shtml Mac (2003-10)
★ ABC Map “abc, iterate a 3D volume preserving system” is another by mathematician J D Meiss. It plots orbit maps of what seems various 3D formulas of significance. I don't quite understand the math here. However, this program is wonderful in that it is like a screensaver with mesmeric images. Dots appears in a 3D box, and these dots fluctuate seemingly ramdomly that forms very distinct patterns. It's like watching statics on TV, but the statics form unpredicable patterns constantly. One can rotate the box. It is a fantastic program even if one knows nothing about the math. The equation it plots has these names: Froeshle, Arnold, ABC, Integrable, Adriana, and others. I hope the author writes a minimum amount of tutorial to benefit the masses.
http://amath.colorado.edu/faculty/jdm/abc.html OSX (2003-10)
IFS Another program by mathematician J D Meiss. This program does the Iterated Function Systems. It comes with a tutorial on IFS. Nice. After reading the one-page tutorial, I understand that IFS is as follows: we have n mappings of the plane. For each iteration, one of them is chosen by a given probability function. So, we start with some points or line in a plane, then apply the functions in each iteration, and plot the transformed points or line accumulatively.
Home page: http://amath.colorado.edu/faculty/jdm/ifs.html Mac (2003-10, 2012)
★ Icon Maker is a simple program that draws orbit maps of the equation
f[z]:=z*(λ + α*z*conjugate[z]+β*Real[z^n]+ω*i)+γ*Conjugate[z]^(n-1)
and other variants. The program is based on ideas in the book Symmetry in Chaos by M Field, M Golubitsky, 1992. This is a wonderful, easy to use, and beautiful program. Author is Jim Burgess.
Home page at http://www.efn.org/~jcburg/software.shtml Mac (2003-10)
Phaser is a commercial program in Java that does simulations of dynamical systems. phaser.com. (2003-12,2010-07-01) Java
Funiter is a program that does iterations for dymical systems study. The author is Stijn Wolters. http://www.funiter.org/ Win (2006-08)