AMMCS-2011 Plenary Talk:

Mathematical Analysis of Neuronal Network Dynamics

by David Cai

New York University

From the perspective of nonlinear dynamical systems, nonequilibrium statistical physics, and scientific modeling, we will review our computational modeling of the dynamics of the primary visual cortex and describe recent developments of mathematical methods used in analysis of the dynamics of neuronal networks arising from the brain.

We will present a kinetic theory approach to study neuronal network dynamics and discuss the interplay between the dynamics over the network and the topology of the network, such as random networks and scale-free networks. Finally we will briefly address the issue of anatomical connectivity and functional connectivity in the brain.

David Cai is currently a professor of mathematics and neural science at Courant Institute of Mathematical Sciences and the Center for Neural Science, New York University. He received his B.S. from Peking University, China, and Ph.D. from Northwestern University, U.S. His research interests include applied mathematics, theoretical physics, and theoretical and computational neuroscience.