一般时移神经元网络模型的弱连通性和强连通性
Weak and strong connectivity regimes for a general time elapsed neuron network model
摘要：
对于大型全连接神经元网络，我们研究了时间流逝模型描述的相互作用的神经元的同质组件的动力学。在一般的假设下，包括在以前的工作[7，8，6]中所做的假设，我们建立了精确的估计的长时间行为的弱和强连接区的情况下，有和没有延迟。我们的结果改进了[7，8]，其中建立了不太准确的估计，并且[6]仅考虑了平滑的发射率。我们的方法结合了在上述以前的作品中引入的几个参数，以及在[13，4]中提出的Weyl和谱映射定理的稍微改进的版本。
英文摘要：
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works [7, 8, 6], we establish accurate estimate on the long time behavior of the solutions in the weak and the strong connectivity regime both in the case with and without delay. Our results improve [7, 8] where a less accurate estimate was established and [6] where only smooth firing rates were considered. Our approach combines several arguments introduced in the above previous works as well as a slightly refined version of the Weyl's and spectral mapping theorems presented in [13, 4].
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