Dynamics and Bifurcations I

Department: 
MATH
Course Number: 
4541
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every fall semester

A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.

Prerequisites: 

MATH 2403 or MATH 2413 or MATH 24X3 or MATH 2552 or MATH 2562 or MATH 2X52

Course Text: 

At the level of Differential Equations, Dynamical Systems, and an Introduction to Chaos by Hirsch, Smale, and Devaney, 3rd edition

Topic Outline: 
  • Scalar Autonomous Equations
  • Elementary Bifurcations
  • Scalar Maps
  • Scalar Nonautonomous Equations
  • Bifurcations of Periodic Equations
  • Planar Autonomous Systems
  • Linear Systems
  • Hopf Bifurcation