Emergence of spatially periodic diffusive waves in small-world neuronal networks
Emergence of spatially periodic diffusive waves in small-world neuronal networks
复制标题
小世界神经元网络中空间周期性扩散波的出现
DOI：
10.1103/physreve.100.042401
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Zhou Douglas
中科院分区：
文献类型：
--
作者：
Gu Qinglong;Xiao Yanyang;Li Songting;Zhou Douglas
实验中观察到脑神经元网络的解剖结构具有小世界网络的特征。然而，小世界结构如何影响网络动态仍有待充分阐明。在这里，我们研究了一类小世界网络的动力学组成的脉冲耦合积分和火灾（I&F）神经元。在随机泊松驱动下，我们发现整个网络的活动类似于扩散波。为了理解其潜在机制，我们分析了由基于发射率的神经元组成的简化正则格型网络，作为原始I&F小世界网络的近似。我们证明了分析和数值，强耦合连接，在没有噪声的情况下，基于发射率的规则晶格网络的活动在空间上形成一个staticgrating模式，对应于在I&F小世界神经元网络中观察到的发射率的空间分布。我们进一步表明，具有不同相位的空间光栅图案包括连续吸引子的I&F小世界和基于发射率的规则晶格网络动力学。在输入噪声存在的情况下，两个网络的活动被扰动沿着连续吸引子，这引起了扩散波。我们的数值模拟和理论分析可能会提供深入的了解在皮层网络中观察到的波模式的产生。
It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a staticgrating patternthat corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.