A Focused Research Group Workshop
Thursday - Sunday, February 3-6, 2005
|Written by Krešimir Josić, University of
The problem of analyzing the behavior of structured networks of
interacting dynamical systems has received much attention recently.
It is of fundamental interest in fields ranging from neuroscience and
genetics to electrical and chemical engineering, and has led to the
development of numerous mathematical techniques. The goal of the
Coupled 60 Workshop was to bring together mathematicians and
theoretical scientists from a variety of fields to exchange ideas on
the subject. It also served as an introduction and overview of the
applications and theory of coupled dynamical systems for the graduate
students and postdoctoral fellows that constituted approximately half
the audience. Moreover, it was an opportunity to mark the 60th
birthdays of five participants: Mike Field, Marty Golubitsky, John
Guckenheimer, Phil Holmes, and Ian Stewart.
|The birthday boys:
Mike Field, Ian Stewart, Marty Golubitsky, Phil Holmes and John
The workshop took place over four days on the campus of the
University of Houston. The talks reflected the variety of problems
and applications of the theory of networks of interacting dynamical
systems. The following is a brief overview. Applications of the
theory of coupled oscillators in neuroscience were discussed by Pete
Ashwin, Paul Bressloff, Jack Cowan, Bard Ermentrout, Phil Holmes,
Nancy Kopell, and Jon Rubin. The Houston Dynamical Systems Group
(Toby Elmhirst, Mike Field, Marty Golubitsky, Krešo Josić,
Matt Nicol, Ian Stewart, Andrew Török) presented their work
on the theory and applications of coupled cell systems, with several
talks focusing on open problems. Different perspectives on the
dynamics of gene networks were given by Gabor Balaszi and Konstantin
Mischaikow. Other participants presented their work on a number of
other topics: celestial mechanics (Jerry Marsden), the analysis of
synchrony in networks (Lou Pecora and Igor Belykh), the driven Van der
Pol oscillator (John Guckenheimer), coupled cell models of solid flame
waves (Bernie Matkowsky) and bifurcations and localization in coupled
cell systems (Martin Krupa and Jeroen Lamb).
The first day of the workshop concluded with a well attended poster
session. The 20+ posters covered a variety of topics, and it was
difficult to visit all of them in one evening. Fortunately, they were
displayed during most of the workshop, and so further discussions were
possible. Many participants headed to the Houston Grand Opera for the
performance of "Il Trovatore" after the second day of the
|From left to right Andrew
Oster, Eric Shea-Brown and Toby Elmhirst.
||Banquet guests listening to Jerry
A banquet held at the Houston Museum of Natural Science concluded
the last full day of the workshop. Dinner followed aperitifs in the
room housing the exceptional mineral collection (recently evaluated by
no other than Steve Smale), and a tour of the butterfly center. This
occasion was also used to mark the 60th birthdays of the five
participants mentioned above. Although the combined output of this
illustrious group would be sufficient to fill a decent library, their
careers and achievements were finely summarized in a presentation by
the Master of Ceremonies Jerry Marsden.
The workshop was sponsored by the National Science Foundation, the
Department of Mathematics and the College of Natural Sciences and
Mathematics at the University of Houston, and was organized by M.
Golubitsky, K. Josić, M. Nicol, and A. Török.