model_2008

model_2008, background information on bifurcation, presented to Lizette Zietsman's Math4974 seminar on Mathematical Modelling, at Virginia Tech, 21 October 2008.

This material was in support of a presentation by Professor Jim Fink of the Computer Science Department at Gettysburg College.

The title of his talk was:

Bifurcation, Catastrophe, Singularity, and All That

The abstract for the talk was:

How did numerical analysts manage to exploit ideas from bifurcation theory, catastrophe theory, and singularity theory to model the dynamics of aircraft flight? In the spirit of the memorable treatise "1066 and All That," this question will be explored with a "fine disregard for annoying details." Despite the intimidating-sounding topics in the title, the talk will be accessible to a general undergraduate audience.

Professor Fink recommends the following book for further information about some of the examples he discussed:

1. Tim Poston, Ian Stewart,
   Catastrophe Theory and its Applications,
   Dover, 1996,
   ISBN13: 978-0486692715,
   LC: QA614.58.P66.

The following files constitute the LaTeX files used to create the background information:

• bifurcation_background.tex, the TeX source code.
• bifurcation_background.pdf, the PDF document.

The following files constitute the LaTeX files used to create the assignment:

• bifurcation_assignment.tex, the TeX source code.
• bifurcation_assignment.pdf, the PDF document.

The following graphics files were used:

• aircraft.png, a PNG image of the coordinate system of an aircraft.
• spring.png, a PNG image of the buckling spring device.
• icam_logo.pdf, a PDF file containing the ICAM logo.