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 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. 2D Flows: Fixed points (Sec. 6.0-6.4)
    2. 2D Flows: Limit cycles (Sec. 7.0-7.3)
    3. 3D Flows: Chaos in Lorenz (Sec. 9.0-9.4)
    4. 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.