Math 431 Dynamical Systems

Course Description

(3-0) 3 credits. Prerequisites: MATH 315 and MATH 321 or permission of instructor. This course is a study of both discrete and continuous dynamical systems. Topics include analysis of planar autonomous systems, stability analysis, bifurcation, chaos, and strange attractors. In addition, this course may include the study of Van der Pol’s equation, Lorenz equations, Duffing’s equation, Hamiltonian systems, and Poincare maps.

Couse Learning Outcomes

A student who successfully completes this course should be able to:

  1. solve systems of linear difference and/or differential equations
  2. model simple physical systems using dynamical systems
  3. apply the existence and uniqueness theorems for ordinary differential equations
  4. generate a phase portrait for a nonlinear one- or two-dimensional dynamical system
  5. construct Lyapunov functions for a continuous dynamical system
  6. locate and describe the bifurcation points for a dynamical system