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Balanced Networks of Spiking Neurons with Spatially Dependent Recurrent Connections

机译：平衡神经网络与空间相关的递归连接的平衡网络

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Networks of model neurons with balanced recurrent excitation and inhibition capture the irregular and asynchronous spiking activity reported in cortex. While mean-field theories of spatially homogeneous balanced networks are well understood, a mean-field analysis of spatially heterogeneous balanced networks has not been fully developed. We extend the analysis of balanced networks to include a connection probability that depends on the spatial separation between neurons. In the continuum limit, we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. Notably, this implies that network models with broad recurrent inhibition are inconsistent with the balanced state. For finite size networks, we investigate the pattern-forming dynamics arising when balanced conditions are not satisfied. Our study highlights the new challenges that balanced networks pose for the spatiotemporal dynamics of complex systems.
机译：具有平衡的反复激励和抑制作用的模型神经元网络捕获皮质中报告的不规则和异步尖峰活动。尽管对空间均匀平衡网络的均场理论已广为人知，但对空间异构平衡网络的均场分析尚未得到充分发展。我们扩展了对平衡网络的分析，以包括取决于神经元之间空间间隔的连接概率。在连续极限中，我们得出稳定，平衡的点火速率解决方案要求外部输入的空间分布要大于循环激励的空间分布，而后者又必须大于或等于循环抑制的空间分布。显然，这意味着具有广泛递归抑制作用的网络模型与平衡状态不一致。对于有限大小的网络，我们研究了不满足平衡条件时出现的图案形成动力学。我们的研究突出了平衡网络对复杂系统的时空动态构成的新挑战。

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