EEG spectral attractors identify a geometric core of resting brain activity

Spectral analysis of electroencephalographic (EEG) data simplifies the characterization of periodic band parameters but can obscure underlying dynamics. By contrast, reconstruction of neural activity in state-space preserves geometric complexity in the form of a multidimensional, global attractor. Here we combine these perspectives, inferring complexity and shared dynamics from eigen-time-delay embedding of periodic and aperiodic spectral parameters to yield unique dynamical attractors for each EEG parameter. We find that resting-state alpha and aperiodic attractors show low geometric complexity and shared dynamics with all other frequency bands, what we refer to as geometric cross-parameter coupling. Further, the geometric signatures of alpha and aperiodic attractors dominate spectral dynamics, identifying a geometric core of brain activity. Non-core attractors demonstrate higher complexity but retain traces of this low-dimensional signal, supporting a hypothesis that frequency specific information differentiates out of an integrative, dynamic core. Older adults show lower geometric complexity but greater geometric coupling, resulting from dedifferentiation of gamma band activity. The form and content of resting-state thoughts were further associated with the complexity of core dynamics. Thus, the hallmarks of resting-state EEG in the frequency domain, the alpha peak and the aperiodic backbone, reflect a dynamic, geometric core of resting-state brain activity. This evidence for a geometric core in EEG complements evidence for a regionally defined dynamic core from fMRI-based neuroimaging, further supporting the utility of geometric approaches to the analysis of neural data.