Complex Systems: Gr Chaos,Fractals&Dynmcal Syst

Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis, and Lorenz equations. Credit not awarded for both CSYS 5766 and MATH 3766. Prerequisite: Graduate student or Instructor permission. Cross-listed with: MATH 5766.

Cross-listed with MATH 5766 A; Open to Degree and PACE students; Prereqs: MATH 2522 or MATH 2544; Total combined enrollment: 35;

This course investigates the mathematical phenomenon of 'chaos' encountered when attempting to predict the future state of any complex system. The Earth's atmosphere represents the hallmark example of chaotic behavior; famously rendered in the metaphor of a butterfly flapping its wings in Brazil setting off a tornado weeks later in Texas. Former undergraduate and graduate students in math, physics, computer science, engineering, biology, and a few other areas have broadened their understanding of mathematical modeling of nonlinear dynamical systems through this course. System behavior that experiences bifurcations from one attracting state to another will be understood from a theoretical, experimental, and numerical perspective.

The course is mainly lecture based, with interaction taking place outside of the class through weekly HW help sessions during office hours. The course requires some experience with Linear Algebra, and programing experience is suggested (but not required).

Weekly assignments (12 total) consist of 5 questions (4 textbook questions and a single programming exercise). There will be a pair of take-home exams at the midpoint and end of the course. HW and Exams are weighted equally. Student projects exploring applications of the material through a recent scientific publication will be presented during the final exam period.