  The mammalian spatial navigation system makes use of several different
sensory information channels. This information is then converted into a neural
code that represents the animal's current position in space by engaging place
cell, grid cell, and head direction cell networks. In particular, sensory
landmark (allothetic) cues can be utilized in concert with an animal's
knowledge of its own velocity (idiothetic) cues to generate a more accurate
representation of position than (idiothetic) path integration provides on its
own (Battaglia et al, 2004). We develop a computational model that merges path
integration with information from external sensory cues that provide a reliable
representation of spatial position along an annular track. Starting with a
continuous bump attractor model, we allow for the possibility of synaptic
spatial heterogeneity that would break the translation symmetry of space. We
use asymptotic analysis to reduce the bump attractor model to a single scalar
equation whose potential represents the impact of heterogeneity. Such
heterogeneity causes errors to build up when the network performs path
integration, but these errors can be corrected by an external control signal
representing the effects of sensory cues. We demonstrate that there is an
optimal strength and decay rate of the control signal when cues are placed both
periodically and randomly. A similar analysis is performed when errors in path
integration arise from dynamic noise fluctuations. Again, there is an optimal
strength and decay of discrete control that minimizes the path integration
error.
