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Applied Dynamical Systems II
ME215B, Winter Quarter 2009

Meets: Tuesday, Thursday 12:30-1:45 Girvetz 1108

Course Description:

This course will cover dynamical systems theory, and the application of dynamical systems techniques to mathematical, physical, biological, and technological systems described by ordinary differential equations or maps. The primary focus will be on dissipative systems, so that the course is complementary to the Advanced Dynamics sequence (ME 201 and 202) which primarily focusses on conservative systems.

Specific topics to be covered include:

  • normal forms
  • bifurcations of fixed points of vector fields
  • bifurcations of fixed points of maps
  • Melnikov's method
  • the Smale horseshoe
  • symbolic dynamics
  • averaging
  • global bifurcations, including homoclinic explosions and Shil'nikov bifurcation
  • Liapunov exponents
  • chaos and strange attractors
  • dynamical systems with delay (guest lectures by Gabor Orosz)
    These topics build on the topics covered in ME215A, Applied Dynamical Systems I.
    Questions? Email Jeff Moehlis at moehlis@engineering.ucsb.edu

    Course Syllabus

    Homework