Final PROJECTS
[due 5/11-13/2009]

Final Project.
Format:
  • An introductory paragraph describing the problem
  • Survey of related work (with references)
  • Derivation of Mathematics
  • Graphics
  • Summary and Conclusions
  • Appendix - Matlab code
  • Appendix - References
It may be submitted as an html, word or pdf file. Total length should be 10-15 pages (if printed on paper)...

Below are listed some ideas of projects for the Final:
  1. Synchronization of Chaos -- When two oscillators are coupled, chaotic effects can be coupled. (ref).
  2. Chaos in physical systems -- For example, the "double pendulum" or the "Belousov-Zhabatinsky" chemical reaction, or possibly "Chaos in Optics" (ref).
  3. Chaos in neural networks -- (ref).

    Attractors in biological systems have proven to be nature's way at optimizing sensitivity and detection in smell (ref).

  4. Fractals in biology -- (ref).

    You would have to come up with some matlab components for this topic...

  5. Chaos and game theory-- (ref).
  6. Chaos and music -- (ref).
  7. Chaos in stochastic models -- We have only talked about deterministic chaos. But introducing a small parameter which comes from a probability density function can make systems stochastic, and will affect the dynamics somewhat. Fractal basins and strange attractors may still exist.
  8. Chaos and the onset of turbulence. Early theories of the onset of turbulent flow were based on bifurcation and period-doubling. Now, there are some theories that state that there is an "attractor" in the Navier Stokes equations which leads to chaos/turbulence. You will need to do some literature search on this one, and the equations are not for the faint-hearted!
  9. Fractal image compression. (ref). Michael Barnsley developed this, holds several patents, and I believe he formed a company to market software (see ref)