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

International audience; Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level inthe brain. Although motivated by biology, these models are phenomenological in nature. They are built on theassumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changesin the underlying synchrony of patterns. It is customary to use spiking neural network models when examiningwithin population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtaininsight from. In this paper, we consider a network ofθ-neurons, which has recently been shown to admit an exactmean-field description in the absence of a spatial component. We show that the inclusion of space and a realisticsynapse model leads to a reduced model that has many of the features of a standard neural field model coupled toa further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysisand numerical continuation software are used to explore the existence and stability of spatiotemporal patternsin the system. In particular, we show that this new model can support states above and beyond those seen in astandard neural field model. These states are typified by structures within bumps and waves showing the dynamicevolution of population synchrony.