The activity in a population of head-direction cells may be visualized as a bump of activity on a ring of cells (0 deg = 360 deg). This stable activity profile can be self-sustained by proper lateral connections. The peak position (representing the internal sense of direction) can be centered anywhere on the ring. When the animal turns its head, the internal activity spot shifts the peak position precisely to mimic the physical movement. I showed that in order to preserve the shape of the traveling activity profile as needed to account for the experimental data, the effective asymmetric connections must have a unique form (derivative rule). To anchor the internal direction to salient landmarks, an additional pattern-recognition mechanism is needed.
This figure is taken from the same paper (J. Neurosci. 1996), showing that a two-dimensional analogy of the contineous-attractor dynamics and the derivative rule for the shift mechanism might apply to hippocampal place cells.