Class 19: Quiz

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