Noise-driven bifurcations in a neural field system modelling networks of grid cells

TL;DR

This paper investigates how small noise levels induce bifurcations in neural field models of grid cells, revealing phase transitions and hysteresis phenomena affecting network activity stability.

Contribution

It demonstrates that noise-driven bifurcations lead to pattern formation in neural networks, providing a mathematical analysis of stability and phase transitions in a PDE-based model.

Findings

Patterns emerge from instability of homogeneous activity at low noise levels

A phase transition occurs as noise decreases, affecting network stability

Hysteresis phenomena are observed near the critical noise value

Abstract

The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity generated by networks of grid cells emerge from the instability of homogeneous activity for small levels of noise. This is carried out by analysing the robustness of network activity patterns with respect to noise in an upscaled noisy grid cell model in the form of a system of partial differential equations. Inhomogeneous network patterns are numerically understood as branches bifurcating from unstable homogeneous states for small noise levels. We show that there is a phase transition occurring as the level of noise decreases. Our numerical study also indicates the presence of hysteresis phenomena close to the precise critical noise value.