This toolbox allows to simulate interactions between neural mass potentials (resonating at 40Hz) in the structural connectome. Here, a single brain region is seen as an oscillator whose dynamics is explained by a Stuart Landau Equation (Hopf Bifurcation including time delay).

Oscillatory models of FHN

A PyTorch-based framework for fitting whole-brain Hopf models to empirical EEG PSD. Optimizes local dynamics and global coupling using structural connectivity and neurotransmitter receptor maps.

This repository contains the analysis pipeline for a cross-condition comparison of whole-brain dynamics between healthy controls (HC) and unmedicated Major Depressive Disorder (MDD), using three independent estimation approaches applied to the Stuart-Landau oscillator — the normal form of a supercritical Hopf bifurcation.

This repository contains the Hopf-GAE, a physics-informed deep learning architecture that detects depression-related dynamical abnormalities without ever training on depressed brains.

Based on the Holling-Tanner predator-prey model, the goal of this project was to analyze data of a population of wolves from Yellowstone National Park in order to determine how to stimulate a healthy oscillatory cycle. Obtaining this value was found through the utilization of linear algebra to find the Hopf bifurcation values of the parameters i…

Numerical analysis and animation of a Kapitza pendulum system as a part of a theoretical mechanics course final project.

This project aims to leverage nonlinear system identification techniques, focusing on the Unscented Kalman Filter (UKF), to enhance modeling and understanding of neural dynamics from fMRI data, addressing the direct challenges of noise and indirect measurement.