The quiz is here: quiz3.pdf
This quiz focuses on Chapters 7 and 8. However, the material in those chapters also requires facility with Chapters 5 and 6.
You may bring notes (front and back of a sheet of paper, handwritten) to this quiz.
- For a planar nonlinear dynamical system
- identify the fixed points
- linearize about them
- use trace/determinant to classify their stability
- for saddles, use eigenvalues and eigenvectors to sketch behavior near the fixed points
- place the linear info on a global phase portrait
- identify limit cycles in systems given in polar coordinates, or argue that such cycles do or do not exist
- identify bifurcations of fixed points and of limit cycles in phase portraits or using analytic criteria
- find a Poincare map at the level of 8.7.1, 8.7.2 or 8.7.9, find an associated periodic orbit, P(y) = y, and use a Floquet multiplier to assess its stability.
- Answer short answer questions about bifurcations in 2D, or other 2D phenomena