Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 415: Applied Dynamical Systems, Chaos and Modeling

Student Body: 

Students in Math, Sciences and Engineering interested in modelling and Chaos

Background and Goals: 

An introduction to nonlinear dynamical systems including stability, bifurcations and chaos. The course will give underlying mathematical ideas, but emphasize applications from many scientific fields.



Subsequent Courses: 


Course Content: 
  • One-dimensional maps and difference equations: linear and nonlinear problems, graphical solutions, bifurcations, chaos.
  • First-order differential equations (one-dimensional flows): linear and nonlinear equations, graphical solutions, bifurcations.
  • Two-dimensional flows: phase plane, stability of fixed points, periodic solutions, and limit cycles. Introduction to bifurcation theory, local and global bifurcations. Tools for studying global behavior of flows: Lyapunov functions, Poincare-Bendixson Theorem, gradient flows.
  • Three-dimensional flows: Lyapunov exponents, Poincare sections, strange attractors, chaos.
3. (N-A)
Math 319 or 320, or consent of instructor.

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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