FIGURE 2 | Extension of the one-dimensional attractor map concept to two dimensions: a model for path integration.
From the following article:
Path integration and the neural basis of the 'cognitive map'
Bruce L. McNaughton, Francesco P. Battaglia, Ole Jensen, Edvard I Moser and May-Britt Moser
Nature Reviews Neuroscience 7, 663-678 (August 2006)
doi:10.1038/nrn1932
Neurons arranged in a plane (a) have interconnections that decline in strength (or probability) monotonically with distance (red arrows). Notice that a boundary problem exists for connections near the edge of the layer of neurons. A solution for this problem is illustrated in Fig. 3. Global feedback inhibition (not shown) keeps the net activity within a narrow range, leading to a focused spot or 'bump' of activity somewhere in the plane (b). The bump can be made to move in correspondence with a rat's motion using an intermediate layer of cells that are conjunctive for position on the plane and head orientation, if the activity of these cells is positively modulated by running speed and the cells encoding a given head direction project asymmetrically to the corresponding side of the cells in the attractor layer from which they receive input. The thresholds are arranged so that these hidden layer cells are silent when there is no motion.
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