Integration properties of the Burak \& Fiete continuous attractor network model

Observed in 2005 by Hafting et al, grid cells are neurons in the medial entorhinal cortex of rats that have the property of firing when the animal is at specific periodic positions in a 2D space such that the map of their activity forms a hexagonal grid pattern. In one of the classes of models that are used to theoretically describe this observation, called continuous attractor networks, a hexagonal pattern present in a neural network is moved accordingly in response to the animal displacement. One of this models, proposed by Burak \& Fiete (2009), uses neurons sensitive to the animal velocity and direction to move this pattern. The network proposed, however, is very well structured in the sense that only four angles (north, south, west and east) are present and that their locations in the network are very specific. In the present study, we compare the model performance when this preferred directions are located at not so organized positions and also when their preferred angle are subjected to noise. Moreover, we also analyze the hexagonal pattern against defective and single bump patterns aiming to show that the first one is less suitable to integrate space displacement in the presence of noise. The hexagonal pattern is the one that maximizes activity in the network and can therefore be more robust to local perturbations.