MATH 717: Applied
Dynamical Systems (Spring 2006)
Instructor:
John Guckenheimer
Meeting
Time & Room
Nonlinear dynamical systems are used as models in every field of science
and engineering. Universal patterns of behavior, including "chaos,''
have been observed in large sets of examples. Mathematical theories describing
geometrically the qualitative behavior of "generic'' systems explain
many of these patterns. This course will discuss both the theory and its
application to examples. Several representative examples from the life
sciences and other disciplines will be described at the beginning of the
course and used throughout the semester to illustrate theoretical ideas.
Emphasis will be placed upon bifurcation, the qualitative changes in solutions
that occur as system parameters are varied. Computational methods for
the analysis of dynamical systems will also be discussed. The performance
of algorithms and their mathematical foundations will be considered. Further
development of these computational methods is an active research area,
and the course lectures will repeatedly deal with this frontier. Computer
laboratory sessions will be held in addition to lectures.
Last modified:
September 26, 2005
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