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Applied Dynamical Systems II
ME215B, Winter Quarter 2007

Meets: Tuesday, Thursday 9:30-10:45 Buchanan Hall Room 1934

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:

  • isochrons and phase response curves
  • averaging
  • coupled oscillators
  • normal forms
  • bifurcations of fixed points of vector fields
  • bifurcations of fixed points of maps
  • the Smale horseshoe
  • symbolic dynamics
  • dynamics near homoclinic points of two-dimensional maps
  • global bifurcations, including homoclinic explosions and Shil'nikov bifurcation
  • Liapunov exponents
  • chaos and strange attractors
  • codimension-two bifurcations
    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