- Series
- Dissertation Defense
- Time
- Tuesday, March 8, 2011 - 9:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Benjamin Webb – School of Mathematics, Georgia Tech
- Organizer
- Benjamin Webb
Real world networks typically consist of a large number of
dynamical units with a complicated structure of interactions. Until recently
such networks were most often studied independently as either graphs or as
coupled dynamical systems. To integrate these two approaches we introduce
the concept of an isospectral graph transformation which allows one to
modify the network at the level of a graph while maintaining the eigenvalues
of its adjacency matrix. This theory can then be used to rewire dynamical
networks, considered as dynamical systems, in order to gain improved
estimates for whether the network has a unique global attractor. Moreover,
this theory leads to improved eigenvalue estimates of Gershgorin-type.
Lastly, we will discuss the use of Schwarzian derivatives in the theory of
1-d dynamical systems.