Nonlinear Physics: Modeling Chaos & Complexity

Jim Crutchfield
chaos@cse.ucdavis.edu; http://cse.ucdavis.edu/~chaos

Spring 2010
WWW: http://cse.ucdavis.edu/~chaos/courses/nlp/

Lecture 4: The Big, Big Picture (Bifurcations I)

Reading: NDAC, Chapter 3.
Topics:

  1. Review last lecture.
  2. Qualitative Dynamics: Space of all dynamical systems
  3. Example: Bifurcations of one-dimensional flows
    1. Saddle Node
    2. Transcritical
    3. Pitchfork
  4. Catastrophes: Fixed point to fixed point bifurcation
  5. Example: Cusp Catastrophe
  6. Catastrophe theory classification of fixed point bifurcations

Reading for next meeting: NDAC, Chapter 8 and Sec. 10.0-10.4.