  The existence and characterisation of noise-driven bifurcations from the
spatially homogeneous stationary states of a nonlinear, non-local
Fokker--Planck type partial differential equation describing stochastic neural
fields is established. The resulting theory is extended to a system of partial
differential equations modelling noisy grid cells. It is shown that as the
noise level decreases, multiple bifurcations from the homogeneous steady state
occur. Furthermore, the shape of the branches at a bifurcation point is
characterised locally. The theory is supported by a set of numerical
illustrations of the condition leading to bifurcations, the patterns along the
corresponding local bifurcation branches, and the stability of the homogeneous
state and the most prevalent pattern: the hexagonal one.
