We study the dynamics of an inhomogeneous neuronal network parametrized by a real number $ \sigma $ and structured by the time elapsed since the last discharge. The dynamics are governed by the parabolic PDE which describes the probability density of neurons with elapsed time $ s $ after its last discharge. We prove existence and uniqueness of a solution to the model. Moreover, we show that under some conditions on the connectivity and the firing rate, the network exhibits total desynchronization.

中文翻译：

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关于具有扩散的神经元网络模型的注释

我们研究了一个不均匀的神经元网络的动力学，该网络由实数$ \ sigma $参数化，并由自上次放电以来经过的时间构成。动力学受抛物线形PDE的支配，该抛物线形的PDE描述了神经元上一次放电后经过的时间$ s $的概率。我们证明了模型解决方案的存在性和唯一性。此外，我们显示出在某些条件下的连通性和触发速率下，网络表现出完全不同步。