# Biomathematics / Computational Biology Colloquium

#### Next generation neural field models

**Speaker:**
Áine Byrne, Center for Neural Science, New York University

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, February 13, 2018, 12:30 p.m.

**Synopsis:**

Neural field models are commonly used to describe bump attractors and wave propagation at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronisation. Unfortunately, these high dimensional models are notoriously hard to gain insight from. In this talk I will consider the theta-neuron model, which has recently been shown to admit to an exact mean-field description for instantaneous pulsatile interactions in the absence of space. I will demonstrate that the inclusion of space and a more realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatio-temporal patterns in the system. In particular, I will show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.