Violation of homogeneity by the vestibulo-ocular reflex of the goldfish

The vestibulo-ocular reflex (VOR) allows animals to maintain stable gaze during head rotations by generating compensatory eye rotations. The VOR is typically tested using sinusoidal head rotation, and VOR gain is calculated as the ratio of the amplitude of eye to head rotational velocity. Through habituation, prolonged exposure to lower frequency sinusoidal head rotation in the dark decreases VOR gain. The VOR has been treated and modeled as a linear system. If it is linear, then the VOR must obey the principle of homogeneity: VOR gain at a particular frequency should be the same regardless of head velocity. We examined the habituated goldfish VOR for homogeneity. We found that it violated this basic principle of linear systems and is therefore non-linear.