|TITLE:||Coupled Systems: Theory and Examples|
|SPEAKER:||Marty Golubitsky (University of Houston)|
|DATE:||Vendredi, 28 Avril 2006|
A coupled cell system is a collection of interacting dynamical systems. Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge. We ask: How much of the qualitative dynamics observed in coupled cells is the product of network architecture and how much depends on the specific equations?
The ideas will be illustrated through a series of examples and theorems. One example shows how a frequency filter / amplifier can be built from a small three-cell feed forward network; and a second illustrates patterns of synchrony in lattice dynamical systems. One theorem gives necessary and sufficient conditions for synchrony in terms of network architecture; and a second shows that synchronous dynamics may itself be viewed as dynamics in a coupled cell system through a quotient construction.
About the speaker Working on the interface between mathematics and applied mathematics, Martin Golubitsky has applied ideas from singularity theory and group theory to bifurcation theory. His research has provided a coherent framework for much work in pattern formation and has been applied by researchers in a wide variety of fields. He has co-authored three widely acclaimed texts on bifurcation theory; the most recent one, "The Symmetry Perspective," received the 2001 Ferran Sunyer i Balaguer Prize. He received his AB from the University of Pennsylvania and his PhD from MIT, and has held appointments at Queens College (CUNY), Arizona State University, and the University of Houston, where he is a Cullen Distinguished Professor of Mathematics. Golubitsky is a Fellow of AAAS and was the 1997 recipient of the Esther Farfel Award (the most prestigious faculty award at the University of Houston). He has been a Rothschild Professor at the University of Cambridge and is currently a Dean's Distinguished Visiting Professor at the University of Toronto. He was the founder and first Editor in Chief of the SIAM Journal on Applied Dynamical Systems. Golubitsky has served on the SIAM, AAAS, and AMS Councils; and is currently President of SIAM.