Paper: The influence of nonlinear resonance on human cortical oscillations

Official MATLAB implementation of the BiSpectral EEG Component Analysis (BiSCA) framework. This repository contains the code to reproduce the analysis and figures presented in our paper.

A longstanding debate in neuroscience concerns whether macroscale brain signals are linear Gaussian processes or harbor nonlinear dynamics. This project introduces BiSCA, a novel framework that unifies power and bispectral analysis to test for nonlinearity in EEG signals.

Our key findings show that:

• The brain's broadband, aperiodic background behaves as a linear, Gaussian process.
• Narrowband oscillatory components, such as the Alpha and Mu rhythms, are the primary sources of cortical nonlinearity, exhibiting significant quadratic cross-frequency coupling.
• There is a striking dissociation between signal power and nonlinearity; the powerful occipital Alpha rhythm is less nonlinear than the parietal Mu rhythm.

This work suggests that nonlinear resonance is a pervasive and crucial feature of cortical signals expressed primarily through resonant oscillations.

• Joint Spectral and Bispectral Modeling: A generalized model that fits the power spectrum and bispectrum simultaneously.
• Nonlinearity Detection: Identifies nonlinear resonance phenomena by modeling harmonically related spectral peaks and their bispectral counterparts.
• Component Decomposition: Additively separates the signal into an aperiodic (linear, Gaussian) Xi (ξ) process and an oscillatory (nonlinear) Rho (ρ) process.
• Statistical Testing: Provides a robust statistical framework for testing the Gaussianity and linearity of each signal component.

To get a local copy up and running, follow these simple steps.

This code is written in MATLAB. The following toolboxes are required to run the analysis:

• Signal Processing Toolbox
• Statistics and Machine Learning Toolbox

1. Clone the repository:

   git clone https://github.com/rigelfalcon/BiSCA.git

2. Open MATLAB, navigate to the cloned directory, and run the setup.m script to add all necessary subdirectories to your MATLAB path:

   setup

To get started, run the example\BiSCA\demo_BiSCA.m script located in the example/BiSCA directory. This script demonstrates how to apply the BiSCA model to sample EEG data and reproduce key figures from the paper.

demo_BiSCA

The scalp EEG and intracranial EEG (iEEG) data analyzed in this study were obtained from the following publications:

• EEG: Li et al. (2022), "Harmonized-Multinational qEEG Norms (HarMNqEEG)". NeuroImage.
• iEEG: Frauscher et al. (2018), "Atlas of the normal intracranial electroencephalogram". Brain.

Please refer to the original publications for information on accessing the datasets.

If you use this code or our findings in your research, please cite our paper:

Wang, Y., Li, M., Reyes, R. G., Bringas-Vega, M. L., Minati, L., Breakspear, M., & Valdes-Sosa, P. A. (2025). Whole brain resting-state EEG dynamics: A mixture of linear aperiodic and nonlinear resonant stochastic processes (p. 2025.06.27.661950). bioRxiv. https://doi.org/10.1101/2025.06.27.661950

@article{Wang2025Whole,
  title={Whole brain resting-state EEG dynamics: A mixture of linear aperiodic and nonlinear resonant stochastic processes},
  author={Wang, Ying and Li, Min and Garc{\'i}a Reyes, Ronaldo and Bringas-Vega, Maria L. and Minati, Ludovico and Breakspear, Michael and Valdes-Sosa, Pedro A.},
  journal={bioRxiv},
  pages={2025.06.27.661950},
  year={2025},
  publisher={Cold Spring Harbor Laboratory}
}

Distributed under the GNU General Public License v3.0. See LICENSE for more information.

Pedro A. Valdes-Sosa - [email protected]

Project Link: https://github.com/rigelfalcon/BiSCA