Center for Neural Science, New York University, New York, New York 10003, USA and Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom.
Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom and Inria Sophia Antipolis Méditerranée Research Centre, MathNeuro Team, 2004 route des Lucioles, Bote Postale 93 06902 Sophia Antipolis, Cedex, France.
Phys Rev E. 2019 Jan;99(1-1):012313. doi: 10.1103/PhysRevE.99.012313.
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 synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of θ-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 spatiotemporal 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.
神经场模型常用于描述大脑组织层面的波传播和凸起吸引子。尽管这些模型是受生物学启发的，但它们本质上是唯象的。它们基于这样的假设，即神经组织在近同步状态下运行，因此无法解释潜在同步模式的变化。在研究群体内同步时，通常使用尖峰神经网络模型。然而，这些高维模型很难提供深入的见解。在本文中，我们考虑了一个θ神经元网络，最近的研究表明，在没有空间成分的情况下，该网络可以得到精确的平均场描述。我们表明，包含空间和现实的突触模型会导致一个简化模型，该模型具有许多标准神经场模型的特征，此外还有一个进一步的动力学方程，描述了网络同步的演化。我们使用图灵不稳定性分析和数值连续软件来探索系统中时空模式的存在和稳定性。特别是，我们表明这个新模型可以支持超出标准神经场模型的状态。这些状态的特点是凸起和波内的结构显示了群体同步的动态演化。
