Guidelines
The purpose of the final project is to give students an opportunity to focus on a particular subject in nonlinear dynamics that they find interesting. For example, the project could be an analysis of an interesting paper or topic in the current scientific literature. It could also be an attempt to apply what you have learned in the class to a particular problem that interests you. In either case you may find it useful to perform your own theoretical or numerical analyses—indeed we encourage it! Analysis of experimental or observational data—or your own experiments or observations!—is also possible. The format is largely unconstrained, but we require the following:
- Submission of your topic and a brief summary (i.e., a short paragraph) by Lecture 20.
- A written report, due on the day of the last class. Brevity (∼1500 words, not including figures or references) is valued over length, but if you need more space to make your point, we’ll read it. We are seeking your personal, critical view of a subject. Of course you should review what’s known or been done, but your creative input is valued above all else.
- A brief (∼3 minute) oral presentation summarizing what you’ve learned, presented during the last meeting of the class.
We strongly advise you to not wait until the last minute to do this. The point of this project is to encourage you to think imaginatively about nonlinear dynamics, and that won’t be possible if you start thinking about the project the day before it is due.
Nonlinear dynamics and its applications throughout science and engineering, and even social science, is a very active area of research. Although our course focuses on the behavior of simple systems with only a few degrees of freedom, much current research focuses instead on more complex systems with many degrees of freedom (ranging, e.g., from a turbulent fluid to a large social network). Please feel free to explore such problems—and if you do, you will find that the concepts and tools you’ve learned in our class will remain useful.
If you need ideas, a good way to start could be to search Google Scholar (scholar.google.com) for some keywords of a subject that interests you in addition to the words “nonlinear dynamics”. Highly cited reviews often provide a good introduction. Though there’s certainly a virtue to focusing on current research, an enormous amount of good work in nonlinear dynamics and chaos, particularly in physical systems, dates to the 1980s and 1990s, and that’s of interest too.
Finally, we’d be happy to talk to you about this and provide suggestions related to your interests—before you choose your topic or after.
Topics Submitted in Fall 2022
- Construction of orbits with prescribed trajectories
- On the utility of non-Newtonian differential equations
- The dynamics of the inverted driven pendulum
- Analysis of current models for whale bubble nets and waveguiding behavior
- A look into the nonlinear dynamics governing the Belousov Zhabotinsky reaction
- Exploring the nonlinear dynamics of ship motion
- Stability estimation through delayed linear representations of partially-observed nonlinear dynamics in neural systems
- Evolutionary game theory
- Understanding rate equation dynamics
- Applications of nonlinear dynamics and chaos to finance
- Understanding treeline as a nonlinear system
- Nonlinear dynamics of natural hazards: forest fires
- Sunspot predictions for solar cycle 25 and non-linear dynamics
- Lyapunov exponents and breast cancer detection
- Double pendulum, Kapitza’s pendulum, and double Kapitza’s pendulum
- An analysis of population dynamics within continuous viral particle production
- Lotka-Volterra predator-prey models
- The three-body problem and its associated nonlinearities
- Analysis of nonlinear dynamics in electric systems
- Chaos and politics
- Thermistors as a model for memristor nonlinear dynamics
- Pseudorandomness and chaos
- Nonlinear behavior of transverse vibration in axially loaded beams
- Exploring ML techniques on prediction of a chaotic system
- Towards a machine-learning-inspired method for computing periodic orbits
- Applying the SINDy algorithm to discover dynamical systems models in geophysical dynamics
