# Pattern phase diagram of spiking neurons on spatial networks

## TL;DR

This paper investigates how spiking neurons on spatial networks form complex patterns and exhibit critical dynamics, revealing a transition from pattern formation to synchrony as network connectivity increases.

## Contribution

It introduces a novel spatiotemporal pattern in neuronal phase fields and characterizes the transition to critical and synchronized states based on network parameters.

## Key findings

- Discovery of a frothing liquid-like spatiotemporal pattern.
- Neuronal avalanche sizes follow a power law with exponent one.
- Identification of metastable behavior before full synchronization.

## Abstract

We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over networks with varying edge density and spatial embedded ness. For intermediate edge density and sufficiently strong spatial embeddedness, we observe a novel spatiotemporal pattern in the field of oscillator phases, visually resembling the surface of a frothing liquid. Increasing the edge density results in critical dynamics, with the distribution of neuronal avalanche sizes following a power law with exponent one. Further increase of the edge density results in metastable behaviour between pattern formation and synchronisation, before transitioning the system entirely into synchrony.