We survey recent analytical approaches to studying the spatiotemporal dynamics of
continuum neural fields. Neural fields model the large-scale dynamics of spatially structured …

Neural field models of firing rate activity have had a major impact in helping to develop an
understanding of the dynamics seen in brain slice preparations. These models typically take …

Recent studies have shown that seizures can spread and terminate across brain areas via a
rich diversity of spatiotemporal patterns. In particular, while the location of the seizure onset …

We study the effect of delays on the dynamics of large networks of neurons. We show that
delays give rise to a wealth of bifurcations and to a rich phase diagram, which includes …

We study a partial integro-differential equation defined on a spatially extended domain that
arises from the modeling of" working" or short-term memory in a neuronal network. The …

This is a book on mathematical neuroscience, in which the unifying theme is wavelike
phenomena at multiple spatial and temporal scales. There are already several excellent …

We review the use of neural field models for modelling the brain at the large scales
necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that …

We develop partial differential equation (PDE) methods to study the dynamics of pattern
formation in partial integro-differential equations (PIDEs) defined on a spatially extended …

In this paper, we introduce a modification of a mean-field model used to describe the brain's
electrical activity as recorded via electroencephalography (EEG). The focus of the present …

In this paper we show how to construct the Evans function for traveling wave solutions of
integral neural field equations when the firing rate function is a Heaviside. This allows a …