  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.
