Complexphase

This directory contains simulation code and visualizations related to the time evolution of geometric and internal phase connections, denoted as ( A(\alpha) ) and ( A(\beta) ), respectively. These simulations support the theoretical framework presented in the manuscript and illustrate dynamic behaviors such as holonomy, phase accumulation, and spike-based encoding.

Contents

• connection_evolution.py
  Simulates the time-dependent behavior of ( A(\alpha) ) and ( A(\beta) ) using complex-valued functions. Outputs include real and imaginary components plotted over time.

• spike_trains.py
  Generates raster plots of spike trains across neurons using the Brian2 simulator. Demonstrates how phase information can be encoded in spike timing.

• figures/
  Contains representative output plots from the simulations, suitable for embedding in the manuscript.

Requirements

• Python 3.8+
• matplotlib
• numpy
• brian2 (for spike train simulation)

Install dependencies with:

pip install matplotlib numpy brian2