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 3: Example Dynamical Systems

Reading: NDAC, Sections 6.0-6.4, 7.0-7.3, and 9.0-9.4.
Topics:

  1. Review last lecture.
  2. Continuous-time ODEs
    1. 1D Flows: Fixed points and their stability (Ch. 2)
    2. 2D Flows: Fixed points and their stability (Sec. 6.0-6.4) (eigensystems)
    3. 2D Flows: Limit cycles (Sec. 7.0-7.3)
    4. 3D Flows: Chaos in Lorenz (Sec. 9.0-9.4)
    5. Simulation Demo
  3. From continuous to discrete time (Sec. 9.4)
    1. Poincaré Maps and Sections
    2. Lorenz ODE to Cusp Map
    3. Rössler ODE to Logistic Map (pp. 376–379)
    4. Discrete-time Maps

Reading for next meeting: NDAC, Chapter 3.