Physics 648: Suggestions for project topics

  1. Flow on circle and synchronization of fire flies (Strogatz, chapter 4)
  2. Flow on circle and simulations to millenium bridge (Strogatz, chapter 4 and Nature paper)
  3. Weakly nonlinear oscillators (start with Strogatz, chapter 7.6)
  4. Choose dynamical system, do bifurcation analysis, and plot phase diagrams
  5. From quasiperiodicity to chaos
  6. Dynamical behavior in a neuron model (for example spiking)
  7. Diverse maps
  8. Phase synchronization and application to simulated data
  9. Phase synchronization and application to real data
  10. Introduction into time-delay differential equation
  11. Nonlinear time series analysis; prediction algorithms
  12. Nonlinear time series analysis; recurrence plots
  13. Embedding and dimension algorithms; application to real data
  14. Embedding and dimension algorithms; application to simulated data
  15. Calculation of fractal (and other) dimensions of cracks or other spatial patterns
  16. How to calculate Lyapunov exponent(s) from data
  17. Spurious Lyapunov exponents
  18. The Lyapunov spectrum
  19. How to numerically determine stable and unstable manifolds
  20. Dynamical systems and noise
  21. Chaos and feedback control
  22. Chaotic scattering
  23. Diffusion-limited aggregation and application
  24. Introduction to cellular automata
  25. Self-organized criticality and the sandpile model
  26. Self-organized criticality and the earthquake model
  27. pattern formation in bird flocks; swarming
  28. "flying to the moon" ... using chaos
  29. Hamiltonian Chaos
  30. Quantum chaos
  31. Firing in coupled neurons
  32. Pattern formation in chemical/biological/physical .. system
  33. Time delay system, e.g. Mackey Glass system
  34. ...
  35. amplitude death in coupled oscillators (oscillation quenching)
  36. cusp catastrophy, or others

  37. see books on syllabus if you are interested in mathematical biology or geophysics models
  38. ...
  39. ... your own project - discuss with me at least 1 week before topic is due -