Boundary effects in the Burak \& Fiete continuous attractor network model

In the search of understanding how the brain processes the position and navigation of an animal, researchers found cells in the hippocampal region that were tuned to positions in space. The first type of cell to be characterized in the 70?s were the place cells, pyramidal cells that are active when the animal is in a particular position in the environment. In 2005 researchers found a yet more intriguing type of cells in an adjacent area called entorhinal cortex, the grid cells. When a rat moves in 2D space, the grid cells fire action potentials according to a hexagonal pattern, covering the environment with a grid of activity. Our study focus on the understanding of a continuous attractor model of grid cells proposed by Burak \& Fiete (2009). In the model the activity in the network is linked to the rat's translation, so that change of position of the rat creates a corresponding displacement of a group of centers of activity in the network. In our study we focus on the boundary properties of the network. Periodic networks integrate better the position compared to aperiodic networks. However periodic networks may present stable pattern of activities with grid defects and in discrete orientations, while aperiodic networks are more flexible in orientation and do not present defects. We also study how the propensity for grid defects of periodic networks depends on the model parameters.