基于脉冲时间响应曲线的平均场理论：含延迟的两个交替神经振荡器种群内部及种群间的同步
Mean Field Theory Based on the Spike Time Response Curve for Synchronization Within and Between Two Alternating Populations of Neural Oscillators with Delays
- Louisiana State University Health Sciences Center – New Orleans（路易斯安那州立大学健康科学中心新奥尔良分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对含延迟的交替神经振荡器种群，提出基于脉冲时间响应曲线的平均场理论，摒弃振荡器相位概念，推导交替放电模式的自洽判据，模拟显示其预测锁相稳定性优于瞬时相移方法，可推广至多类耦合场景。
AI中文摘要：
为研究由离散时刻发射的脉冲耦合的振荡器，通常假设每个脉冲的效应是瞬时相移，发射与接收间可能存在传导延迟。但我们关注的是神经振荡器，其中每个脉冲（动作电位）会激活双指数突触，且在高频下，突触电导的持续时间可能大于网络周期，因此接收脉冲的效应可在多个周期内累加。为克服此局限，我们此前针对单个同步种群定义了平均场方法，本文将其扩展至两个交替同步种群，假设来自其中一个同步种群的单个振荡器的扰动由单个自连接神经振荡器表示。每个振荡器发射的延迟双指数突触序列被分为紧张性（tonic）和位相性（phasic）分量。由于输入具有连续而非脉冲的性质，我们需摒弃振荡器相位的概念，仅基于时间间隔偏离稳态值的扰动，推导两个同步种群间交替放电模式存在性与稳定性的自洽判据。模拟结果表明，对于上述定义的高频振荡，该平均场方法比瞬时相移方法能更好地预测两个同步种群间锁相的存在性与稳定性，此方法或可推广至非神经振荡器间的其他耦合形式。
英文摘要：
In order to study oscillators coupled by pulses emitted at discrete times, it is generally assumed that the effect of each pulse is an instantaneous phase shift, with a possible conduction delay between emission and receipt. However, we are interested in neural oscillators in which each pulse (action potential) activates a biexponential synapse, and at high frequencies, the duration of the synaptic conductance may be greater than the network period. Therefore, the effect of received pulses can summate over the course of several cycles. To overcome this limitation, we previously defined a mean field approach for a single synchronous population. Here, we extend it to two alternating synchronous populations by assuming a perturbation of a single oscillator from one of the synchronous populations which is represented by a single self-connected neural oscillator. The train of delayed biexponential synapses emitted by each oscillator is divided into a tonic and a phasic component. Because of the continuous rather than pulsatile nature of the input, we had to drop the concept of oscillator phase and derive self-consistent criteria for the existence and stability of an alternating firing pattern between two synchronous populations based solely on the perturbation of time intervals from their steady state values. Simulations showed that for high frequency oscillations as defined above, the mean field approach predicts the existence and stability of phase-locking between two synchronous populations better than the instantaneous phase shift approach. This approach may generalize to other forms of coupling amongst non-neural oscillators.
