Whole brain resting-state EEG dynamic: A mixture of linear aperiodic and nonlinear resonant stochastic processes

A longstanding debate in neuroscience concerns whether macroscale brain signals can be described as purely linear Gaussian processes or they harbor the more complex statistics of nonlinear dynamics. We introduce BiSpectral EEG Component Analysis (BiSCA), a framework unifying power spectral and bispectral analysis to test for nonlinearity by identifying inter-frequency harmonic relationships and disambiguating them from superimposed components. In particular, simulations confirm that it is able to separate valid nonlinearity from non-Gaussianity, which is a common confound. Applying this test to two large human brain recordings datasets (1,771 intracranial channels and 960 individuals scalp EEG), we find the brains broadband, aperiodic background behaves as a linear, Gaussian process, while narrowband Rho oscillatory --including the Alpha and Mu rhythms --are the primary source of cortical nonlinearity, exhibiting significant quadratic cross-frequency coupling. Both recordings show significant departures from linear Gaussian behavior. We observe a clear dissociation between signal power and nonlinearity. While the occipital Alpha rhythm dominates the power spectrum, the strongest nonlinear signatures arise from the less dominant parietal Mu rhythm. These findings suggest that nonlinear resonance is pervasive in cortical signals, primarily expressed through resonant oscillations rather than aperiodic activity. Without accounting for these intrinsic nonlinear interactions, a principled understanding of neural activity will be incomplete.