Teaching :: Nonlinear Dynamical Systems (AM 114/214)

Research Projects

Research Projects

The AM 114/214 projects can be original research or an in-depth report of an existing paper. The research report of the project must be handed in on the last day of class. Hereafter is a list of potential research topics. 

  1. Order-chaos transition in planar elastic pendulum (paper) 
  2. Deep learning for early warning signals of tipping points (paper)
  3. Controlling nonlinear dynamical systems into arbitrary states using machine learning (paper)
  4. Physics-Guided Deep Learning for Dynamical Systems (paper)
  5. Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods (paper)
  6. Data-driven identification of nonlinear dynamical systems (paper)
  7. Synchronization of metronomes (paper)
  8. Approximation of flow maps and probability distributions using deep neural networks  (report)
  9. Discovering governing equations from data (paper)
  10. Koopman operators and nonlinear dynamical systems (paper1, paper2)
  11. Vortex induced vibrations of circular cylinder (paper)
  12. Deep learning of nonlinear dynamics using time-stepping constraints (paper)
  13. Data-driven discovery of Koopman eigenfunctions for control (paper)  
  14. Computing Poicaré maps (paper)
  15. Computing flow maps (paper1, paper2, paper3)  
  16. Instabilities and mixing in 2D Kolmogorov flow (paper)
  17. Chaotic phase similarities in damped-driven oscillators (paper1, paper2) 
  18. Hamiltonian dynamical systems and the N-body problem (book1, book2)
  19. Chaos in the Lorenz-96 model (paper)
  20. Modeling walker synchronization on the Millenium bridge (paper)
  21. Huygens synchronization of two clocks (paper1, paper2)
  22. Chaotic advection in laminar incompressible fluid flows (paper)
  23. Synchronization in nonlinear dynamical systems (paper1, paper2, book)
  24. Chaos control and schedule of shuttle buses (paper)
  25. Parametrization of global attractors in finite- and infinite-dimensional dynamical systems (paper1, paper2)
  26. Encouraging moderation: clues from a simple model of ideological conflict (paper)
  27. A right handed world and the dominance of left-handed athletes (paper)
  28. Cats protecting birds: modelling the mesopredator release effect (paper)
  29. Modelling language death (paper)
  30. Bifurcation analysis of fluid flows  (paper1, paper2, paper3)