Title: Homeostasis, Catastrophes, and Networks
Speaker: Martin Golubitsky
Abstract: Networks consisting of nodes and unidirectional arrows encode systems of differential equations. The arrows indicate which nodes are coupled to which. The nodes and arrows can be annotated to indicate which nodes are identical and which kinds of coupling are identical. We discuss how the network architecture (the annotated graph) affects the kinds of solutions we see in coupled networks of differential equations.
In applications what distinguishes a coupled network of differential equations from a large system of differential equations in the desire to keep track of the output from each node individually. It is then possible to compare signals from different nodes (synchrony) and to keep track of singularities in individual nodes. The talk will discuss two applications illustrating these ideas: binocular rivalry and homeostasis.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy students can sign up for this lecture series by registering for one or two credit hours of Math 6193, class #9226 (with Prof H. Moscovici).
