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) and (MATH 1522 or MATH 1553 or MATH 1554 or MATH 1564 or MATH 1502 or MATH 1512)

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