Visual stimuli produce waves of activity in the visual cortex of
freshwater turtles. The waves can be visualized using modern imaging
methods and have complicated spatiotemporal dynamics. Waves can be
simulated in a largescale model of the visual cortex. These
simulations suggest that the waves consist of several components. It
would be important to understand the nature of the transitions
between the components, and it is natural to approach the problem
using dynamical systems theory. However, the model consists of more
than 20,000 coupled, nonlinear ordinary differential equations with
on the order of 100,000 parameters. This seminar will discuss an
approach to reducing the dimensionality of the system by modeling the
cortex as a family of linear, nonautonomous ordinary differential
equations with on the order of 50 parameters. The stability of the
system can be studied using the Lyapunov theory of nonautonomous
systems. The analysis shows that the system has a single stable
fixed point, but several metastable states.
