Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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Syllabus

Summary:
This course will cover dynamical systems theory, and the application of dynamical systems techniques to mathematical, physical, biological, and technological systems described by ordinary differential equations or maps. The primary focus will be on dissipative systems, so that the course is complementary to the Advanced Dynamics sequence (ME 201) which primarily focus on conservative systems.
Instructor:
Igor Mezic
Engineering II 2339
Tel: 893-7603
e-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it
Lecture Hours: Mon – Wed 11:00-12:15 in Buchanan 1934.
Office Hours: Mon -Wed 12:30-2:00, Engineering II 2339.
Homeworks: Weekly [link].
Textbook: Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd Edition, Springer-Verlag.
Midterm exams: 1. Grading policy: Homeworks 20 %, Midterm 30 %, Final 50 %.
Topics(chapters are from the textbook by Wiggins)
  • fixed points for vector fields and maps, and their stability properties (Ch. 1, Liapunov functions (Ch. 2)
  • invariant manifolds for linear and nonlinear systems (Ch. 3)
  • periodic orbits (Ch. 4)
  • index theory (Ch. 6)
  • asymptotic behavior, attractors (Ch. 8)
  • Poincaré-Bendixson Theorem (Ch. 9)
  • Poincaré maps (Ch. 10 and 11)
  • structural stability (Ch. 12)
  • center manifolds (Ch. 18)
  • normal forms (Ch. 19)
  • bifurcations of fixed points of vector fields (Ch. 20, 22)
  • Melnikov’s method (Ch. 28)
  • the Smale horseshoe (Ch. 23)
  • symbolic dynamics (Ch. 24)
  • chaos and strange attractors (Ch. 30).
Recommended Literature and references:
  • J. Guckenheimer and P. Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields”
  • S. H. Strogatz, “Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering”
  • P. Glendinning, “Stability, Instability, and Chaos”, http://www.scholarpedia.org
Last Updated on Tuesday, 02 October 2012 13:25  

Acknowledgements