Neural networks generate a variety of rhythmic activity patterns, often involving different timescales. One example arises in the respiratory network in the pre-Bötzinger complex of the mammalian brainstem, which can generate the eupneic rhythm associated with normal respiration as well as recurrent low-frequency, large-amplitude bursts associated with sighing. Two competing hypotheses have been proposed to explain sigh generation: the recruitment of a neuronal population distinct from the eupneic rhythm-generating subpopulation or the reconfiguration of activity within a single population. Here, we consider two recent computational models, one of which represents each of the hypotheses. We use methods of dynamical systems theory, such as fast-slow decomposition, averaging, and bifurcation analysis, to understand the multiple-timescale mechanisms underlying sigh generation in each model. In the course of our analysis, we discover that a third timescale is required to generate sighs in both models. Furthermore, we identify the similarities of the underlying mechanisms in the two models and the aspects in which they differ.

中文翻译：

---

节律性呼吸神经元模型中叹气爆发和加息的时标和机制。

神经网络产生各种有节奏的活动模式，通常涉及不同的时标。一个例子出现在哺乳动物脑干的伯森格前复合体的呼吸网络中，它可以产生与正常呼吸有关的心律失常以及与叹息相关的反复的低频大振幅猝发。提出了两个相互竞争的假说来解释叹气的产生：神经元群体的募集不同于产生心律失常的亚群或单个群体内活动的重新配置。在这里，我们考虑两个最近的计算模型，其中一个代表每个假设。我们使用动力学系统理论的方法，例如快慢分解，求平均值和分叉分析，了解每个模型中产生叹气的多种时间尺度机制。在我们的分析过程中，我们发现两个模型都需要第三时间尺度来产生叹气。此外，我们确定了两个模型中潜在机制的相似性以及它们之间不同的方面。