Newhall Katherine A, Shkarayev Maxim S, Kramer Peter R, Kovačič Gregor, Cai David
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250, USA.
Department of Physics and Astronomy, Iowa State University, 12 Physics Hall, Ames, Iowa 50011-3160, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 May;91(5):052806. doi: 10.1103/PhysRevE.91.052806. Epub 2015 May 11.
We study the synchronization of a stochastically driven, current-based, integrate-and-fire neuronal model on a preferential-attachment network with scale-free characteristics and high clustering. The synchrony is induced by cascading total firing events where every neuron in the network fires at the same instant of time. We show that in the regime where the system remains in this highly synchronous state, the firing rate of the network is completely independent of the synaptic coupling, and depends solely on the external drive. On the other hand, the ability for the network to maintain synchrony depends on a balance between the fluctuations of the external input and the synaptic coupling strength. In order to accurately predict the probability of repeated cascading total firing events, we go beyond mean-field and treelike approximations and conduct a detailed second-order calculation taking into account local clustering. Our explicit analytical results are shown to give excellent agreement with direct numerical simulations for the particular preferential-attachment network model investigated.
我们研究了一个基于电流的随机驱动积分发放神经元模型在具有无标度特性和高聚类性的优先连接网络上的同步情况。同步是由级联的全发放事件引起的，网络中的每个神经元在同一时刻发放。我们表明，在系统保持这种高度同步状态的情况下，网络的发放率完全独立于突触耦合，仅取决于外部驱动。另一方面，网络维持同步的能力取决于外部输入的波动和突触耦合强度之间的平衡。为了准确预测重复级联全发放事件的概率，我们超越了平均场和树状近似，并考虑局部聚类进行了详细的二阶计算。对于所研究的特定优先连接网络模型，我们明确的解析结果与直接数值模拟结果显示出极好的一致性。
