The stability of synchronous states is analyzed in the context of two populations of inhibitory and excitatory neurons, characterized by two different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable class of sparse random matrices, randomness being a consequence of the network structure. A detailed analysis, which includes also the study of finite-amplitude perturbations, is performed in the limit of narrow pulses, finding that the overall stability depends crucially on the relative pulse-width. This has implications for the overall property of the asynchronous (balanced) regime.

中文翻译：

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稀疏神经元网络中同步状态的稳定性

在两个抑制性和兴奋性神经元群体的背景下分析了同步状态的稳定性，其特征在于两个不同的脉冲宽度。问题减少到确定合适类别的稀疏随机矩阵的特征值的问题，随机性是网络结构的结果。在窄脉冲的限制下进行了详细的分析，其中还包括有限幅值扰动的研究，发现整体稳定性主要取决于相对脉冲宽度。这对异步（平衡）机制的整体属性有影响。