神经元群体中棘突间隔的非稳态动力学
Non-stationary dynamics of interspike intervals in neuronal populations
AI总结：
本文研究了神经元群体中棘突间隔的非稳态动力学，通过群体密度框架推导了二维福克-计划方程和一维矩方程，分析了外部输入和网络振荡对棘突间隔分布的影响。
摘要：
我们使用群体密度框架研究了整合-放电神经元群体中膜电位和上次放电时间的联合动力学。这导致了一个二维福克-计划方程，能够捕捉完整神经元状态的演变，同时伴随一组一维方程，用于描述棘突间隔（ISI）的矩。该形式允许我们表征时间依赖的ISI分布，即使在远离稳态的群体中，例如在时间变化的外部输入或网络振荡期间。通过在稳态状态下进行微扰展开，我们还推导出ISI分布对弱输入调制的解析表达式。
英文摘要：
We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the evolution of the full neuronal state, along with a one-dimensional hierarchy of equations for the moments of the inter-spike interval (ISI). The formalism allows us to characterize the time-dependent ISI distribution, even when the population is far from stationarity, such as under time-varying external input or during network oscillations. By performing a perturbative expansion around the stationary state, we also derive an analytic expression for the linear response of the ISI distribution to weak input modulations.
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