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I-AIM Interdisciplinary Seminar
3:10 PM Friday Nov 26 in SS 5017A (100 St. George Street)
Professor Martin Golubitsky (University of Houston Department of Mathematics)
"COUPLED CELL SYSTEMS: THEORY AND EXAMPLES"
A coupled cell system is a collection of individual, but interacting,
dynamical systems. Coupled cell models assume that the output from
each cell is important --- not just the dynamics considered as a whole.
In these systems the signals from two or more cells can be compared
and patterns of activity can emerge. We ask when can the cell dynamics
in a subset of cells be identical (synchrony) or differ by a phase shift.
In particular: How much of the qualitative dynamics observed in coupled
cells is the product of network architecture and how much is related to
the specific dynamics of cells and the way they are coupled?
We illustrate the ideas through a series of examples and discuss three
theorems. The first theorem classifies spatio-temporal symmetries of
periodic solutions (and has application to central pattern generators
for animal gaits); the second gives necessary and sufficient conditions
for synchrony in terms of network architecture; and the third shows that
synchronous dynamics may itself be viewed as a coupled cell system through
a quotient construction. This project is joint with Ian Stewart.
Refreshements to follow in the adjacent Math Lounge.
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