Wave Turbulence and Cortical Dynamics

Abstract

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.