Brain Wave Dynamics in Hopfield-Kuramoto Model

This repository contains the implementation of the Hopfield-Kuramoto model for simulating multi-wave phase patterns in brain dynamics, as described in the paper:

"Brain wave dynamics in a Hopfield-Kuramoto model"
Ruwei Yao, Yichao Li, Xintong Yao, Kang Wang, Jingling Qu, Xiaolong Zou, and Bo Hong
School of Biomedical Engineering, Tsinghua University, Beijing, China
Published in Physical Review E, 2025
DOI: 10.1103/PhysRevE.111.044310

Overview

This project implements a computational framework that:

• Models brain wave dynamics using a modified Kuramoto model with heterogeneous connectivity strength
• Encodes multiple wave phase patterns as attractors via Hebbian-like learning
• Simulates large-scale brain wave patterns observed in fMRI data
• Provides tools to analyze stability, bifurcations, and dynamic landscapes

Features

• Pattern Encoding: Store multiple wave phase patterns as stable attractors
• Connectivity Control: Adjust eigenvalues to control pattern dominance/stability
• Bifurcation Analysis: Study high-dimensional bifurcations in attractor networks
• fMRI Modeling: Reproduce dominant wave patterns from human brain imaging data
• Visualization: Tools for phase pattern visualization and analysis