Cortical neural networks maintain autonomous electrical activity called spontaneous activity that represents the brain’s dynamic internal state even in the absence of sensory stimuli. The spatio-temporal complexity of spontaneous activity is strongly related to perceptual, learning, and cognitive brain functions; multi-fractal analysis can be utilized to evaluate the complexity of spontaneous activity. Recent studies have shown that the deterministic dynamic behavior of spontaneous activity especially reflects the topological neural network characteristics and changes of neural network structures. However, it remains unclear whether multi-fractal analysis, recently widely utilized for neural activity, is effective for detecting the complexity of the deterministic dynamic process. To verify this point, we focused on the log-normal distribution of excitatory postsynaptic potentials (EPSPs) to evaluate the multi-fractality of spontaneous activity in a spiking neural network with a log-normal distribution of EPSPs. We found that the spiking activities exhibited multi-fractal characteristics. Moreover, to investigate the presence of a deterministic process in the spiking activity, we conducted a surrogate data analysis against the time-series of spiking activity. The results showed that the spontaneous spiking activity included the deterministic dynamic behavior. Overall, the combination of multi-fractal analysis and surrogate data analysis can detect deterministic complex neural activity. The multi-fractal analysis of neural activity used in this study could be widely utilized for brain modeling and evaluation methods for signals obtained by neuroimaging modalities.

皮层神经网络维持称为自发活动的自主电活动，即使在没有感觉刺激的情况下，它也代表大脑的动态内部状态。自发活动的时空复杂性与感知、学习和认知大脑功能密切相关；多重分形分析可用于评估自发活动的复杂性。最近的研究表明，自发活动的确定性动态行为尤其反映了拓扑神经网络特征和神经网络结构的变化。然而，目前还不清楚最近广泛用于神经活动的多重分形分析对于检测确定性动态过程的复杂性是否有效。为了验证这一点，我们专注于兴奋性突触后电位 (EPSP) 的对数正态分布，以评估具有 EPSP 对数正态分布的尖峰神经网络中自发活动的多重分形。我们发现尖峰活动表现出多重分形特征。此外，为了研究尖峰活动中确定性过程的存在，我们针对尖峰活动的时间序列进行了替代数据分析。结果表明，自发的尖峰活动包括确定性的动态行为。总的来说，多重分形分析和替代数据分析的结合可以检测确定性的复杂神经活动。