LINKS & LISTINGS
    

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