Stability and Bifurcation Theory

AMCS 390D. Stability and Bifurcation Theory, Fall 2014, KAUST
Instructor: Aslan Kasimov
Lectures:  9:00-10:30 every Tuesday and Thursday in Room 9-4222

Prereqs: Basic courses in calculus and differential equations
Recommended: AMCS 231 or AMCS 201. 
The course is an introduction to the theory of stability and nonlinear dynamics of systems described by ordinary and partial differential equations. Topics include: equilibrium solutions and their stability, invariant manifolds, bifurcations, periodic orbits and their stability, Poincare maps, center manifolds, normal forms, chaos and its characterization. Applications to problems arising in physics, engineering, and biology.

Required texts:

  1. S. Strogatz, Nonlinear dynamics and chaos. (2nd edition is coming in the Summer 2014).

The final grade will be based on homework (~40%) and midterm exams (~60%).

The primary text is by Strogatz. Most of the course deals with ODE, introducing essential theoretical and numerical tools required to understand their solutions. The last several lectures will make a transition to PDE.