Abstract The analysis of electroencephalographic (EEG) activity has historically been dominated by linear approaches centred on spectral decomposition and the quantification of signal power within predefined frequency bands. While these methods have played a fundamental role in the development of contemporary neuroscience, they exhibit important limitations when applied to nonlinear, non-stationary, and highly complex systems such as the human brain. In this work, a new methodological framework is introduced, based on the combined use of the Hurst exponent and the Hilbert–Huang Transform, hereafter referred to as the Hurst–Hilbert–Huang (HHH) framework. The proposed approach begins with the local estimation of the Hurst exponent over band-filtered EEG signals, yielding a derived time series that captures the temporal evolution of the system’s order–chaos balance. This second-order time series is subsequently analysed using the Hilbert–Huang Transform, allowing for a time–frequency representation that does not correspond to classical neuronal oscillations. Instead, the HHH spectrogram enables the visualisation of the variational dynamics of the frequency of reorganisation of the brain order–chaos balance, an emergent, second-order observable that cannot be accessed through traditional spectral or wavelet-based methods (Hurst, 1951; Huang et al., 1998; Díaz & Córdova, 2021). Representative results obtained from multichannel EEG recordings during a visual reasoning task are presented, revealing structured, reproducible spatio-temporal patterns across cortical regions, as well as systematic differences between low-beta and high-beta activity. Finally, a set of quantitative descriptors derived from the HHH spectrogram is proposed, organised into an individual dynamic profile of the brain order–chaos balance. Keywords: EEG, order and chaos, Hurst exponent, brain entropy, Hilbert–Huang, complex systems.
Díaz et al. (Thu,) studied this question.