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 5: The Big, Big Picture (Bifurcations) II

Reading: NDAC, Chapter 8 and Sec. 10.0-10.4.
Topics:

  1. Review last lecture.
  2. Bifurcations in ODEs (Simulation demos):
    1. Hopf bifurcation
    2. Limit cycle to torus
    3. Torus to chaos
    4. Chaos to chaos
    5. Period-doubling route to chaos
  3. Return maps return
  4. 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

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