We propose a model for the control of fixational eye movements using time-delayed random walks. Fixational eye movements produce random displacements of the retinal image to prevent perceptual fading. First, we demonstrate that a transition from persistent to antipersistent correlations occurs in data recorded from a visual fixation task. Second, we propose and investigate a delayed random-walk model and get, by comparison of the transition points, an estimate of the neurophysiological delay. Differences between horizontal and vertical components of eye movements are found which can be explained neurophysiologically. Finally, we compare our numerical results with analytic approximations.

• Received 2 August 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.138104