M641, Spring 2003: Ordinary Differential Equations
TR 2
Instructor: Dr. Iuliana Oprea

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Prerequisites: M640 or the consent of the instructor

S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos,
Springer Verlag, Texts in Applied Matehmatics, 2, 3-rd Edition 1997.

J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical systems,
and Bifurcations of Vector Fields, Springer, NY, 5-th Edition 1997.

-Background material from dynamical systems theory
-Poincare Maps: theory, construction, examples
-Center manifolds and normal forms
-Local bifurcations: bifurcations of fixed points
-Some aspects of global bifurcations and chaos

Miscellaneous links:

  1. World of Bifurcation
  2. BU page on ODEs
  3. Nicholas B. Tufillaro, Jeremiah Reilly, and Tyler Abbott , An experimental approach to nonlinear dynamics and chaos
  4. Andrea Milani Comparetti, INTRODUZIONE  AI SISTEMI DINAMICI, Dipartimento di Matematica, Università di Pisa
  5. M. Cross, Chaos on the Web
  6. The Double Well Oscillator