Figure 4.

Sensory cue interaction as phase-code feedback. (A) The spatial profile of cue interaction C_cue is a circular Gaussian field (Eq. 4) oriented at some position on the track (dotted line). Example cue is 15° (SD) wide and centered at 0°. (B) Schematic circuit diagram of the abstract phase feedback mechanism (Eq. 5) for a single oscillator from the VMO population. The ith VMO is decomposed into its phase variable θ_i and output waveform. The phase of every oscillator receives the same velocity (v) and sensory (C_cue) inputs, and has an oscillator-specific feedback target depending on the current (closest) cue on the track. Phase targets are learned by path integration during the first lap. The phase difference between the ongoing (θ) and target (þeta*) phase offsets is gain modulated (×) by the strength of the cue. (C) Illustration of VMO synchronizing to a phase target. (Simplified for purposes of illustration, see Figure 5 for simulation and analysis output.) Top two panels: without feedback, constant phase offsets (top) yield out-of-phase oscillations (bottom). Bottom three panels: idealized cue interaction (top) modulates VMO phase offset (middle) so that its oscillation becomes phase synchronized with the target (bottom).