Neural field model of memory-guided search.

Many organisms can remember locations they have previously visited during a search. Visual search experiments have shown exploration is guided away from these locations, reducing redundancies in the search path before finding a hidden target. We develop and analyze a two-layer neural field model that encodes positional information during a search task. A position-encoding layer sustains a bump attractor corresponding to the searching agent's current location, and search is modeled by velocity input that propagates the bump. A memory layer sustains persistent activity bounded by a wave front, whose edges expand in response to excitatory input from the position layer. Search can then be biased in response to remembered locations, influencing velocity inputs to the position layer. Asymptotic techniques are used to reduce the dynamics of our model to a low-dimensional system of equations that track the bump position and front boundary. Performance is compared for different target-finding tasks.