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A brief description about what the program does is given. For a more detailed description,
see the source code and/or read the relevant sections, on this website. Some links in here
take you to subsections that describe the code and gives the relevant pointer to the
download site!!
There is a simple set of programs that I used to make the plots for the tutorial
on logistic map, the tarred gzipped
file contains a program feigen.c which calculates the Feigenbaum constant using
the super critical orbits. The program is short and simple but the logic and
the analytic behind is subtle. Check it out! From the point of view of model
based control strategy, we have a java applet
demonstration of both linear (Occasional
proportional feedback control) and a nonlinear control method applied to the
case of chaotic Logistic map.
There are set of four programs that can be
used as a template for a simulation of ordinary differential equations (ODEs).
To keep the code simple the program outputs only phase varibales. The
actual implementation is done for Rossler system and the programs are
rossler.c - implementation of 4th order
Runge-Kutta method.
ros-retmap.c - return map for the
Rossler system by taking the Poincare section when 'x' is maximum (Uses what
is called the Henon's trick for the exact location the Poincare section).
ros-bif.c - Bifurcation diagram for the
Rossler system at the Poincare section (the surface is as defined above).
ros-bif.c - Chaotic mixing in Rossler
attractor. (Click here to see the animation).
The following code implements Henon map system with XWindow Motif widgets.
You don't need to have the commercial Motif library on your system.
I have the gnu version called Lesstif and was
successfully compiled on my Linux machine. A simple demonstration of Recursive
proportional Feedback algorithm as appllied to Henon map is given here.
The bouncing ball code
bball.c is a simple C program that simulates
a freely falling ball under the influence gravity and it also demonstrates
the reconstruction of the chaotic attractor using impact time interval. The program was
used to plot the 3-D embedding of the attractor, bifurcation diagram and the phenomenon
of crisis. The XWindow based interactive version is more
elaborate in the sense that it implements the
control algorithm (RPF) in conjunction with adaptive learning algorithm. The
implementation of control algorithm is general in the sense that it assumes no
knowledge of the model and thus can be directly applied to control data from an
experimental system. The program besides many other things allows real time 3-D
visualization of the attractor
is possible and one can rotate the coordinate system about any of the X-, Y-
or Z- axes. The
DOS version does exactly the same thing.
The program used for the presentation of N-ball
falling freely under gravity with motion constrained along the vertical direction
and balls with different masses and stationary "table"
is given here. This is probably the only
program downloadable from this website which demonstrates chaos in Hamiltonian system.
As a simple
test of the high dimensional adaptive recursive proportional feedback (HDARPF) control
algorithm with tracking through the parameter space, there is an implementation for
the case of Henon map. This is written
with X-Window graphics interface. A full blown actual implementation of our HDARPF
algorithm, implemented on a Hyper-chaotic Rossler attractor, is Windows based
program, with various options. The executable
with documentation will be soon made available. The program additionally allows data
acquisition from an experimental setup via National Instruments - ATMIO-16E data
acquisition board and allow real time control of an actual experimental system.
The program runs both in model or data acquisition mode.
The following is one single tarred gzipped
source code and executable for the software
developed between 96-99 as a part of my doctoral thesis. The programs basically
simulate a sinusoidally driven linear oscillator impacting against two stationary
symmetrically placed walls (you can change it to one wall dynamically)
a nonlinear oscillator impacting against a sinusoidally driven wall and
a 1-D chain of globally driven linear oscillators coupled due to collision
between them.
The top level directory structure is SHO MW and chain, respectively.
See the readme file for the details of the program contained in there. Most of the
details and explanation can be found from the subsection on
impact oscillator in ORDER & CHAOS section of this
web page. Each subdirectory contains a bin directory which
has three statically linked executables for Linux/alpha machine, Linux/i386
machine and the solaris/Sun machine. The makefiles are provided
and for the most part you may need to correct the library path for X-Window based
graphics routines.
The individual directories can be had from here.
Nonlinear Pendulum impacting a Moving Wall (MW)
Driven Linear Oscillator Constrained by staionary walls
Spatio-temporal chaos in globally driven impact coupled SHOs
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