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DSWeb Tutorials Competition '07
By Evelyn Sander
George Mason University
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This year DSWeb ran a student competition for
tutorials on dynamical systems. The first such contest took place in
2005 (as reported in the July, 2005
issue of this magazine). Prizes were awarded to Christian Kuehn
of Cornell University and John Wordsworth of Exeter University. Both
winning entries are published in the DSWeb Tutorials section. Kuehn and Wordsworth
received a cash prize and a travel award to attend the SIAM Conference
on Applied Dynamical Systems in Snowbird, Utah. Dwight Barkley,
Charlie Doering, Bard Ermentrout, Mary Silber, and Mary Lou Zeeman
served as judges.
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Evelyn Sander gives prizes to
John Wordsworth (middle) and Christian Kuehn (right) at the DSWeb
Student Competition awards ceremony at the SIAM Conference on Applied
Dynamical Systems in Snowbird, Utah, May, 2007; photo by Hinke
Osinga. |
Christian Kuehn's tutorial
An Introduction to
Rotation Theory is an excellent supplement for a basic dynamical
systems course for mathematics students. The text includes exercises
with hints and answers, as well as animated images to make this work
as a self-paced tutorial for a beginning student. The topics start out
quite simply with an introduction to circle maps and rotation
numbers. However, the discussion progresses quickly to quite advanced
topics, such as the relationship between rotation numbers and ergodic
theory, omega-limit sets, and wandering intervals. There is also a
discussion of Denjoy theory for irrational rotation numbers, followed
by an introduction to Arnol'd tongues for families of
diffeomorphisms. Amazingly, such sophisticated topics are presented
without making the tutorial unreadable for a beginning student with an
undergraduate analysis background. The tutorial contains many
references, including links to other online material.
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An animated image from
Christian Kuehn's tutorial illustrates the rotation number for circle
maps. |
John Wordsworth's
An Introduction to
Coupled Oscillators: Exploring the Kuramoto Model is a good
introduction to coupled oscillators for novice students in dynamical
systems. It does not assume any analysis background, which would make
it well suited to any science students. It gives a derivation of the
Kuramoto model, a discussion of the phase response curve, the nature
of the Hopf bifurcations occuring for weakly coupled oscillators, and
a description of synchronization that occurs at a critical parameter
of coupling. There are many graphical images to clarify explanations,
but the most compelling piece is an excellent interactive Kuramoto
simulator for experimentation, with suggestions of interesting
experiments to try. The tutorial ends with further suggestions for
modifications, as well as a set of references.
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John Wordsworth's tutorial
includes an interative simulation of a Kuromoto
oscillator. |
This contest was limited to graduate students.
However, DSWeb encourages contributions to the Tutorials Section from
all members of the dynamical systems community. A link on DSWeb
spreads the word about your interactive tutorial. It is also a good
way to share lecture notes or talks with the rest of the
community.