Early olfactory pathway responses to the presentation of an odor exhibit remarkably similar dynamical behavior across phyla from insects to mammals, and frequently involve transitions among quiescence, collective network oscillations, and asynchronous firing. We hypothesize that the time scales of fast excitation and fast and slow inhibition present in these networks may be the essential element underlying this similar behavior, and design an idealized, conductance-based integrate-and-fire model to verify this hypothesis via numerical simulations. To better understand the mathematical structure underlying the common dynamical behavior across species, we derive a firing-rate model and use it to extract a slow passage through a saddle-node-on-an-invariant-circle bifurcation structure. We expect this bifurcation structure to provide new insights into the understanding of the dynamical behavior of neuronal assemblies and that a similar structure can be found in other sensory systems.

早期嗅觉通路对气味呈现的反应在从昆虫到哺乳动物的整个门中表现出非常相似的动态行为，并且经常涉及静止、集体网络振荡和异步发射之间的过渡。我们假设这些网络中存在的快速激发和快速和慢速抑制的时间尺度可能是这种类似行为背后的基本要素，并设计了一个理想化的、基于电导的积分和发射模型，以通过数值模拟验证这一假设。为了更好地理解跨物种的共同动力学行为背后的数学结构，我们推导出了一个发射率模型，并使用它来提取通过鞍节点上一个不变圆分岔结构的缓慢通道。