论文标题
$ q $ - 高斯异质性的神经种群的平均场方程
Mean-field equations for neural populations with $q$-Gaussian heterogeneities
论文作者
论文摘要
长期以来，使用低维模型来描述大型神经种群的集体动力学长期以来一直是理论神经科学中的一项有吸引力的任务。最近开发的还原方法使得可以直接从单个神经元的微观动力学中得出此类模型。为了简化降低，通常假定为异质网络参数假定凯奇分布。在这里，我们扩展了由$ Q $ -Gaussian分销定义的更广泛的异质性类别的简化方法。此分布的形状取决于tsallis索引$ q $，并随着该指数的变化而逐渐从凯奇分布变为普通高斯分布。我们为具有$ q $ - 高斯分布式兴奋性参数的二次集成神经元的抑制网络得出平均场方程。结果表明，网络的动态模式显着取决于由Tsallis索引确定的分布形式。从平均场方程获得的结果通过微观模型的数值模拟证实。
Describing the collective dynamics of large neural populations using low-dimensional models for averaged variables has long been an attractive task in theoretical neuroscience. Recently developed reduction methods make it possible to derive such models directly from the microscopic dynamics of individual neurons. To simplify the reduction, the Cauchy distribution is usually assumed for heterogeneous network parameters. Here we extend the reduction method for a wider class of heterogeneities defined by the $q$-Gaussian distribution. The shape of this distribution depends on the Tsallis index $q$ and gradually changes from the Cauchy distribution to the normal Gaussian distribution as this index changes. We derive the mean-field equations for an inhibitory network of quadratic integrate-and-fire neurons with a $q$-Gaussian distributed excitability parameter. It is shown that the dynamic modes of the network significantly depend on the form of the distribution determined by the Tsallis index. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.
