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Neural field models are commonly used to describe wave propagation and bumpattractors at a tissue level in the brain. Although motivated by biology, thesemodels are phenomenological in nature. They are built on the assumption thatthe neural tissue operates in a near synchronous regime, and hence, cannotaccount for changes in the underlying synchrony of patterns. It is customary touse spiking neural network models when examining within populationsynchronisation. Unfortunately, these high dimensional models are notoriouslyhard to obtain insight from. In this paper, we consider a network of$\theta$-neurons, which has recently been shown to admit an exact mean-fielddescription in the absence of a spatial component. We show that the inclusionof space and a realistic synapse model leads to a reduced model that has manyof the features of a standard neural field model coupled to a further dynamicalequation that describes the evolution of network synchrony. Both Turinginstability analysis and numerical continuation software are used to explorethe existence and stability of spatio-temporal patterns in the system. Inparticular, we show that this new model can support states above and beyondthose seen in a standard neural field model. These states are typified bystructures within bumps and waves showing the dynamic evolution of populationsynchrony.

A next generation neural field model: The evolution of synchrony within patterns and waves