PHY 28A
Natural Computation and Self-Organization:
The Physics of Information Processing in Complex Systems

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

Winter
WWW: http://csc.ucdavis.edu/~chaos/courses/poci/

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

Reading: NDAC, Chapter 3
Topics:

  1. Qualitative dynamics: Space of all dynamical systems
  2. Example: Bifurcations of one-dimensional flows
    1. Saddle node
    2. Transcritical
    3. Pitchfork
  3. Catastrophe theory
    1. Catastrophes: Fixed point to fixed point bifurcation
    2. Example: Cusp Catastrophe
    3. Catastrophe theory classification of fixed point bifurcations

Reading: NDAC, Chapter 8 and Secs. 10.0-10.4.