Pyzza Pamela B, Newhall Katherine A, Kovačič Gregor, Zhou Douglas, Cai David
Department of Mathematics and Statistics, Kenyon College, Gambier, OH USA.
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC USA.
Cogn Neurodyn. 2021 Feb;15(1):103-129. doi: 10.1007/s11571-020-09640-3. Epub 2021 Jan 15.
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不同门类中表现出显著相似的动力学行为，并且经常涉及静息、集体网络振荡和异步放电之间的转变。我们假设这些网络中存在的快速兴奋以及快速和慢速抑制的时间尺度可能是这种相似行为背后的关键因素，并设计了一个理想化的、基于电导的积分发放模型，通过数值模拟来验证这一假设。为了更好地理解跨物种共同动力学行为背后的数学结构，我们推导了一个发放率模型，并用它来提取通过不变圆上鞍结分岔结构的慢速过程。我们期望这种分岔结构能为理解神经元集合的动力学行为提供新的见解，并且在其他感觉系统中也能发现类似的结构。
