标题： 波浪湍流和皮层动力学 显示英文标题

标题： Wave Turbulence and Cortical Dynamics

摘要： 通过脑电图（EEG）和脑磁图（MEG）记录的皮层活动反映了跨越多个时间和空间尺度的复杂动力学。 这些信号的频谱分析一致显示出幂律行为，这是湍流系统的特征。 在本文中，我们基于波湍流理论推导出神经场活动的动力学方程，强调能量和伪粒子密度如何通过直接和逆向级联在波空间（k空间）中流动。 我们探讨了不同形式的非线性，特别是三波和四波相互作用如何塑造光谱特征，包括谐波生成、光谱色散和瞬态动力学。 虽然实证数据中观察到的幂律衰减总体上与湍流级联一致，但不同研究中的差异，如双衰减率或谐波结构的存在，表明了潜在机制的多样性。 我们认为，尽管没有单一模型能完全解释所有光谱观测结果，但关键约束条件出现了：即皮层动力学表现出与涉及单级联和双级联以及三波和四波相互作用的湍流波系统一致的特征。 这种基于湍流的框架为解释大规模脑活动提供了一个有原则且统一的方法，包括状态转换和癫痫动力学。 显示英文摘要

摘要： Cortical activity recorded through EEG and MEG reflects complex dynamics that span multiple temporal and spatial scales. Spectral analyses of these signals consistently reveal power-law behaviour, a hallmark of turbulent systems. In this paper, we derive a kinetic equation for neural field activity based on wave turbulence theory, highlighting how quantities such as energy and pseudo-particle density flow through wave-space (k-space) via direct and inverse cascades. We explore how different forms of nonlinearity, particularly 3-wave and 4-wave interactions, shape spectral features, including harmonic generation, spectral dispersion, and transient dynamics. While the observed power-law decays in empirical data are broadly consistent with turbulent cascades, variations across studies, such as the presence of dual decay rates or harmonic structures, point to a diversity of underlying mechanisms. We argue that although no single model fully explains all spectral observations, key constraints emerge: namely, that cortical dynamics exhibit features consistent with turbulent wave systems involving both single and dual cascades and a mixture of 3- and 4-wave interactions. This turbulence-based framework offers a principled and unifying approach to interpreting large-scale brain activity, including state transitions and seizure dynamics.