Simon Fraser University Department of Mathematics
Spring 2003

MATH 467-3: Dynamical Systems

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Nonlinear Dynamics and Bifurcation

This course is an introduction to the study of dynamical systems. Nonlinear differential equations and iterative maps arise in the mathematical description of numerous systems throughout science and engineering, for instance in physics, chemistry, biology, economics, and elsewhere. Such systems may display complicated and rich dynamical behaviour, and we will develop some linear and nonlinear mathematical tools for their analysis, and consider models in such fields as population biology, ecology, and mechanical and electrical oscillations. Our emphasis throughout will be on the qualitative behaviour of the models, in particular, on the prediction of qualitative change in the nature of the dynamics as a system parameter varies (bifurcation).

In this course we will proceed from simpler to more complicated (and more interesting!) systems. We begin with one-dimensional flows, their steady states, stability and bifurcations, and then observe the far more complicated dynamics, including chaos, that may occur in one-dimensional maps. Phase-plane analysis in two dimensions reveals the possibility of oscillations and limit cycles, and we study their bifurcations. As time permits, we will also investigate higher-dimensional dynamical systems, deterministic chaos and strange attractors.


Instructor: Ralf Wittenberg
Office: K-10536; Tel: 291-4792
E-Mail: ralfw@sfu.ca
Office Hours: Monday, 2:30-3:30pm in K-10536; Wednesday 2:30-3:20pm in AQ 5016 (until 4:30pm in K-10536); or by appointment (preferably by e-mail)
Lecture: Monday, Wednesday, Friday 12:30-1:20pm
Location: AQ 2104
Web Page: http://www.math.sfu.ca/~ralfw/math467w03
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Text: Steven H. Strogatz,
"Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering"
Westview Press.

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