Neural fields: from derivation to two-dimensional patterns.

Speaker: Kevin Green

Affiliation: UOIT

The human brain is a notoriously complicated system.  The reality of the situation is that we have a very large number of neurons, with an even larger number of synaptic connections between them determining its dynamics.  Modelling the brain, or even parts of it, as a sum of individual neurons is a near-intractable problem, pushing on our current limits of computational sophistication.  Perhaps it makes sense to approximate the large-scale dynamics of a discrete neural network with some form of averaged dynamics in a continuous limit: a neural population, or neural field.

This talk will give an overview of how to build continuous (in space and time) models of neural activity.  Using some physiological considerations, we show how the synaptic coupling of neural populations can be expressed as an Integro-differential term over space and time.   A summary of past analyses of such models will be given: wave, bump and pulse solutions, and pattern-forming bifurcations.  Finally, our recent results on analysis and simulation of wave-forming instabilities in two-dimensional space are presented.