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Applied Dynamical Systems II
ME215B, Winter Quarter 2017

Meets: Tuesday, Thursday 12:30 - 1:45PM Engr II Bldg Room 2243

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 covers conservative systems.

Specific topics to be covered include:

  • bifurcation of fixed points of vector fields
  • bifurcations of fixed points of maps
  • the Smale horseshoe
  • symbolic dynamics
  • Liapunov exponents
  • Takens-Bogdanov bifurcations
  • Melnikov's method
  • global bifurcations, including homoclinic explosions and Shil'nikov bifurcation
  • averaging
  • phase models / coupled oscillators
  • canards
  • dynamical systems with symmetry
    These topics build on the topics covered in ME215A, Applied Dynamical Systems I.
    Questions? Email Jeff Moehlis at moehlis@engineering.ucsb.edu

    Course Syllabus