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 5: Bifurcations II

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

  1. Review last lecture.
  2. Logistic map
  3. Fixed point to limit cycle
  4. Phenomenon and calculation
  5. Limit cycle to limit cycle
  6. Phenomenon and calculation
  7. Routes to chaos: Period-doubling cascade
  8. Phenomenon and calculation
  9. Band-merging
  10. Periodic windows and intermittency
  11. Simulation demo
  12. Bifurcations in ODEs:
    1. Hopf bifurcation
    2. Limit cycle to torus
    3. Torus to chaos
    4. Chaos to chaos

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