Dynamical Systems Analysis of Visual Cortex

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 large-scale 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, non-linear 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, non-autonomous ordinary differential equations with on the order of 50 parameters. The stability of the system can be studied using the Lyapunov theory of non-autonomous systems. The analysis shows that the system has a single stable fixed point, but several metastable states.