标题： 下一代神经场模型：模式和波浪中同步性的演化 显示英文标题

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

摘要： 神经场模型常用于描述大脑组织水平上的波传播和突触吸引子。 尽管这些模型受到生物学的启发，但它们本质上是现象学的。 它们建立在神经组织处于接近同步状态的假设之上，因此无法解释模式底层同步性的变化。 在研究种群内同步性时，通常使用尖峰神经网络模型。 不幸的是，这些高维模型很难获得洞察。 在本文中，我们考虑了一个$\theta$-神经元的网络，该网络最近被证明在没有空间成分的情况下可以接受精确的平均场描述。 我们表明，引入空间和现实的突触模型会导致一个简化模型，该模型具有标准神经场模型的许多特征，并耦合了一个进一步的动力学方程，用于描述网络同步性的演化。 使用图灵不稳定性分析和数值延续软件来探索系统中时空模式的存在性和稳定性。 特别是，我们展示了这个新模型可以支持超出标准神经场模型所见的状态。 这些状态以突触块和波中的结构为特征，显示了种群同步性的动态演化。 显示英文摘要

摘要： Neural field models are commonly used to describe wave propagation and bump attractors 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 obtain insight from. In this paper, we consider a network of $\theta$-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a 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, we 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.