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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 the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and… (More)

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 discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The… (More)

We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a… (More)

A dynamical theory of spike train transitions in networks of pulse-coupled integrate-and-fire (IF) neural oscillators is presented. We begin by deriving conditions for 1:1 frequency locking in a network with non-instantaneous synaptic interactions. This leads to a set of phase equations determining the relative firing times of the oscillators and the… (More)

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from… (More)

The hippocampus, and particularly the CA3 and CA1 areas, exhibit a variety of oscillatory rhythms that span frequencies from the slow theta range (4-10 Hz) up to fast ripples (200 Hz). Various computational models of different complexities have been developed in an effort to simulate such population oscillations. Nevertheless the mechanism that underlies… (More)

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 is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of… (More)

- Stephen Coombes, Carlo Laing
- Philosophical transactions. Series A…
- 2009

In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the… (More)