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