Modeling the network dynamics of pulse-coupled neurons
Modeling the network dynamics of pulse-coupled neurons
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DOI：
10.1063/1.4977514
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发表时间：
2017-03-01
期刊：
影响因子：
2.9
通讯作者：
Ott, Edward
中科院分区：
文献类型：
--
作者：
Chandra, Sarthak;Hathcock, David;Ott, Edward
为了研究不同网络度分布和度相关性（重复性）的影响，我们推导出脉冲耦合θ神经元的大型网络的宏观动力学的平均场近似。使用Ott和Antonsen [Chaos 18，037113（2008）]的分析，我们得到了一个描述平均场动力学的简化常微分方程组，与系统的完整动力学方程组相比，具有显着更低的维数。我们发现，对于足够大的网络和度，约化系统的动力学行为与全网络的动力学行为一致。这种降维允许系统相变和吸引子的有效表征。对于具有紧密峰值度分布的网络，宏观行为与其他人先前研究的全连通网络非常相似。相比之下，具有高度偏斜度分布的网络由于不同振子的度依赖行为的出现而表现出不同的宏观动力学。对于非连续网络（即，没有度相关性的网络），我们观察到存在一个同步点火阶段，该阶段可以通过网络中的双折射或双折射来抑制。我们表明，这里得到的结果可以用来分析网络拓扑结构对神经网络的宏观行为的影响，在一个计算效率高的方式。出版社：AIP Publishing
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations), we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion. Published by AIP Publishing.