School of Mathematical Sciences, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.
Phys Rev E. 2019 Oct;100(4-1):042401. doi: 10.1103/PhysRevE.100.042401.
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 static grating pattern that 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.
在实验中观察到，大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力学仍有待充分阐明。在这里，我们研究了一类由脉冲耦合积分-点火（I&F）神经元组成的小世界网络的动力学。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放率的神经元组成的简化规则晶格网络，作为原始 I&F 小世界网络的近似。我们通过理论和数值分析表明，在强耦合连接的情况下，在没有噪声的情况下，基于发放率的规则晶格网络的活动在空间上形成一个静态光栅图案，对应于在 I&F 小世界神经元网络中观察到的发放率的空间分布。我们进一步表明，不同相位的空间光栅图案构成了 I&F 小世界和基于发放率的规则晶格网络动力学的连续吸引子。在存在输入噪声的情况下，两个网络的活动都沿着连续吸引子受到干扰，这导致了扩散波。我们的数值模拟和理论分析可能为理解皮质网络中观察到的波模式的产生提供了一些见解。
