Mathematical studies of networks of excitatory and inhibitory neurons

Jack Cowan (Mathematics and Neurology, University of Chicago, USA)

Abstract: Since the 1940s there have been many attempts to model the behaviour of networks of excitatory and inhibitory neurons, with applications to many areas of neuroscience. I will provide a brief overview of some of these attempts, but will focus on only two applications, (a) vision and (b) spontaneous brain activity. In part (a) I will contrast the receptive field paradigm and its consequences, with what can be learned from a study of the perception of geometric visual hallucinations. In part (b) I will look at the topic of criticality in large-scale brain activity, in particular self-organized criticality, and will show details of how one uses mathematics to illuminate both applications.