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

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

Winter 2008
WWW: http://cse.ucdavis.edu/~chaos/courses/ncaso/

Lecture 4: The Big, Big Picture (Bifurcations)

Reading: NDAC, Chapter 3, Chapter 8, and Secs. 10.0-10.4.
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
  4. Bifurcations in discrete-time maps: Logistic map
  5. Fixed point to limit cycle
  6. Phenomenon and calculation
  7. Limit cycle to limit cycle
  8. Phenomenon and calculation
  9. Routes to chaos: Period-doubling cascade
  10. Phenomenon and calculation
  11. Band-merging
  12. Periodic windows and intermittency
  13. Simulation demo

Reading for next meeting: NDAC, Sec. 12.0-12.3, 9.3, and 10.5.