Stability of two dimensional spiking attractor network models of grid cells

Stellate cells in rat medial entorhinal cortex (MEC) are important for the neural representation of location [1]. As an animal moves through its environment, they fire in locations that together form a periodic lattice, or grid, of activity. Each vertex of the lattice is surrounded by a hexagon of other vertices. The periodic response remains stable even in the absence of visual and olfactory cues [1]. Such coding provides a representation of space within the area an animal can explore [2].
While the precise mechanisms of information processing in the MEC are not known, it has been suggested that in order for the spatial position of the rat to be updated in the grid cell network, information about the rat's movement must be processed from the head direction input system [3]. Path integration, the integration of linear and angular self motion of the rat, could potentially be sufficient to account for the grid cell response. The existence of head direction cells and speed modulated responses of grid and head direction cells support this idea [3].