# On interplay between excitability and geometry

## TL;DR

This paper investigates how excitability levels influence wave-front propagation and pattern formation in geometrically constrained excitable media, using numerical simulations of the FitzHugh-Nagumo model.

## Contribution

It reveals the role of excitability in controlling wave behavior in complex geometries and explores wave dynamics on random planar graphs.

## Key findings

- Localized wave-fragments propagate ballistically at lower excitability.
- Excitability affects wave propagation through angled branches and sudden expansions.
- Patterns of wave traversal depend on excitability levels.

## Abstract

A commonly accepted feature of an excitable medium is that a local excitation leads to a propagation of circular or spiral excitation wave-fronts. This is indeed the case in fully excitable medium. However, with a decrease of an excitability localised wave-fragments emerge and propagate ballistically. Using FitzhHugh-Nagumo model we numerically study how excitation wave-fronts behave in a geometrically constrained medium and how the wave-fronts explore a random planar graph. We uncover how excitability controls propagation of excitation in angled branches, influences arrest of excitation entering a sudden expansion, and determines patterns of traversing of a random planar graph by an excitation waves.