Physics 648: Suggestions for project topics

- Flow on circle and synchronization of fire flies (Strogatz, chapter 4)
- Flow on circle and simulations to millenium bridge (Strogatz, chapter 4 and Nature paper)
- Weakly nonlinear oscillators (start with Strogatz, chapter 7.6)
- Choose dynamical system, do bifurcation analysis, and plot phase diagrams
- From quasiperdiodicity to chaos
- Dynamical behavior in a neuron model (for example spiking)
- The Henon map
- Phase synchronization and application to simulated data
- Phase synchronization and application to real data
- Introduction into time-delay differential equation
- Nonlinear time series analysis; prediction algorithms
- Nonlinear time series analysis; recurrence plots
- Embedding and dimension algorithms; application to real data
- Embedding and dimension algorithms; application to simulated data
- Calculation of fractal (and other) dimensions of cracks or other spatial patterns
- How to calculate Lyapunov exponent(s) from data
- Spurious Lyapunov exponents
- The Lyapunov spectrum
- How to numerically determine stable and unstable manifolds
- Dynamical systems and noise
- Chaos and feedback control
- Chaotic scattering
- Diffusion-limited aggregation and application
- Introduction to cellular automata
- Self-organized criticality and the sandpile model
- Self-organized criticality and the earthquake model
- pattern formation in bird flocks
- "flying to the moon" ... using chaos
- Hamiltonian Chaos
- Quantum chaos
- Firing in coupled neurons
- Pattern formation in chemical/biological/physical .. system
- ...

- see books on syllabus if you are interested in mathematical biology or geophysics models

- ...
- ... your own project - discuss with me at least 1 week before topic is due -