MATH 7170: Applied Dynamical Systems (Fall 2011)

Instructor: John Guckenheimer

Prerequisite: MATH 4200 or a comparable course on differential equations. (MATH 6170 and/or 6180 are not necessary.)

The focus of this course is on theory and algorithms that can be used to analyze dynamical system models from across the sciences. Bifurcations — qualitative changes that occur in the dynamics of a system as parameters are varied — and the analysis of chaotic attractors are central themes in the course. Additional material beyond the text, Nonlinear Oscillations, Dynamical Systems and Bifiurcations of Vector Fields by Guckenheimer and Holmes, will depend upon student interest. Past topics have included the role of symmetry in analyzing bifurcations, numerical methods for solving ordinary differential equations and computing bifurcations, and multiple time scale dynamical systems.