We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N --> infinity. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.

中文翻译：

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具有缓慢适应的兴奋性神经元网络中的波动驱动的节律发生。

我们研究了 N 个尖峰神经元的兴奋性全对全耦合网络，具有突触过滤的背景噪声和缓慢的活动依赖性超极化电流。这种系统在噪声强度（方差）和细胞兴奋性水平的值范围内表现出噪声诱导的突发振荡。由于这两个量都取决于背景突触输入的速率，因此我们展示了噪声如何提供一种机制来增加有节奏的爆发的鲁棒性和爆发频率的范围。通过利用时间尺度的分离，我们还展示了如何将系统动力学简化为极限 N --> 无穷大中的低维平均场方程。对平均场方程的分岔结构的分析提供了对引发和终止爆发的动力学机制的见解。