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.

Alternatives: 

N/A

Subsequent Courses: 

N/A

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.
credits: 
3. (N-A)
semester: 
Fall
prereqs: 
MATH 376, (MATH 234 and 319), (MATH 234 and 320), (MATH 234 and 340), (MATH 234 and 341) or (MATH 234 and 375) or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) program

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

(608) 263-3054

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