The collective electrophysiological dynamics of the brain as a result of sleep-related biological drives in Drosophila are investigated in this paper. Based on the Huber-Braun thermoreceptor model, the conductance-based neurons model is extended to a coupled neural network to analyze the local field potential (LFP). The LFP is calculated by using two different metrics: the mean value and the distance-dependent LFP. The distribution of neurons around the electrodes is assumed to have a circular or grid distribution on a two-dimensional plane. Regardless of which method is used, qualitatively similar results are obtained that are roughly consistent with the experimental data. During wake, the LFP has an irregular or a regular spike. However, the LFP becomes regular bursting during sleep. To further analyze the results, wavelet analysis and raster plots are used to examine how the LFP frequencies changed. The synchronization of neurons under different network structures is also studied. The results demonstrate that there are obvious oscillations at approximately 8 Hz during sleep that are absent during wake. Different time series of the LFP can be obtained under different network structures and the density of the network will also affect the magnitude of the potential. As the number of coupled neurons increases, the neural network becomes easier to synchronize, but the sleep and wake time described by the LFP spectrogram do not change. Moreover, the parameters that affect the durations of sleep and wake are analyzed.

中文翻译：

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果蝇与睡眠相关生物驱动的神经网络的集体动力学

本文研究了果蝇中与睡眠有关的生物驱动的大脑的集体电生理动力学。基于Huber-Braun热感受器模型，将基于电导的神经元模型扩展到耦合神经网络，以分析局部场电势（LFP）。通过使用两个不同的指标来计算LFP：平均值和与距离有关的LFP。假设电极周围神经元的分布在二维平面上具有圆形或网格分布。无论使用哪种方法，都能获得与实验数据大致相符的定性相似结果。在唤醒过程中，LFP有不规则或规则的峰值。但是，LFP在睡眠期间会定期爆裂。为了进一步分析结果，小波分析和栅格图用于检查LFP频率如何变化。还研究了不同网络结构下神经元的同步。结果表明，在睡眠期间大约在8 Hz处有明显的振荡，而在唤醒过程中则没有。可以在不同的网络结构下获得LFP的不同时间序列，并且网络的密度也将影响电势的大小。随着耦合神经元数量的增加，神经网络变得更容易同步，但是LFP频谱图描述的睡眠和唤醒时间不会改变。此外，分析了影响睡眠和唤醒时间的参数。结果表明，在睡眠期间大约在8 Hz处有明显的振荡，而在唤醒过程中则没有。可以在不同的网络结构下获得LFP的不同时间序列，并且网络的密度也将影响电势的大小。随着耦合神经元数量的增加，神经网络变得更容易同步，但是LFP频谱图描述的睡眠和唤醒时间不会改变。此外，分析了影响睡眠和唤醒时间的参数。结果表明，在睡眠期间大约在8 Hz处有明显的振荡，而在唤醒过程中则没有。可以在不同的网络结构下获得LFP的不同时间序列，并且网络的密度也将影响电势的大小。随着耦合神经元数量的增加，神经网络变得更容易同步，但是LFP频谱图描述的睡眠和唤醒时间不会改变。此外，分析了影响睡眠和唤醒时间的参数。随着耦合神经元数量的增加，神经网络变得更容易同步，但是LFP频谱图描述的睡眠和唤醒时间不会改变。此外，分析了影响睡眠和唤醒时间的参数。随着耦合神经元数量的增加，神经网络变得更容易同步，但是LFP频谱图描述的睡眠和唤醒时间不会改变。此外，分析了影响睡眠和唤醒时间的参数。