Biological Cybernetics manuscript No. (will be inserted by the editor) Henning U. Voss · Bruce D. McCandliss · Jamshid Ghajar · Minah Suh · CNRC-TBI group A quantitative synchronization model for smooth pursuit target tracking Received: date / Accepted: date Abstract We propose a quantitative model for human smooth pursuit tracking of a continuously moving visual target which is based on synchronization of an internal expectancy model of the target position coupled to the retinal target signal. The model predictions are tested in a smooth circular pursuit eye tracking experiment with transient target blanking of variable duration. In sub- jects with a high tracking accuracy, the model accounts for smooth pursuit and repeatedly reproduces quantita- tively characteristic patterns of the eye dynamics during target blanking. In its simplest form, the model has only one free parameter, a coupling constant. An extended model with a second parameter, a time delay or memory term, accounts for predictive smooth pursuit eye move- ments which advance the target. The model constitutes an example of synchronization of a complex biological system with perceived sensory signals. Keywords Smooth pursuit · Synchronization · Dy- namical Modeling 1 Introduction The human eyes can perform two distinctive forms of mo- tion: Rapid movement of the eye from one fixation point to another, known as saccadic movement, and smooth pursuit eye movements which is much slower and allow us Henning U. Voss Citigroup Biomedical Imaging Center, Weill Medical College of Cornell University, 1300 York Avenue, Box 234, New York, NY 10021, USA, Tel.: 001 (212) 746 5781, Fax.: 001 (212) 746 6681, E-mail: hev2006@med.cornell.edu Bruce D. McCandliss, Sackler Institute for Developmental Psychobiology, Weill Medical College of Cornell University, New York, N.Y. · Jamshid Ghajar, Brain Trauma Foundation and Dept. of Neurological Surgery, Weill Medical College of Cornell University, New York, N.Y. · Minah Suh, Dept. of Neurological Surgery, Weill Medical College of Cornell Uni- versity, New York, N.Y. · CNRC-TBI group, Cognitive and Neurobiological Research Consortium in Traumatic Brain In- jury to stabilize the images from moving objects on the retina, thereby enabling us to perceive the moving objects in de- tail. Contrary to saccades during which vision is highly deteriorated, vision is maintained during smooth pur- suit. It is well-known and intriguing that smooth eye movements normally cannot be induced voluntarily but require a continuously moving object in the visual field [47,27,34,32]. In the theory of synchronization of dy- namical systems this fact could be seen in a new light: If smooth pursuit depended on synchronization between an internal model for the object position as part of a driven system (the oculomotor system) coupled to a driving sys- tem (the object), smooth eye movements would become impossible with the absence of a smoothly moving ob- ject. Smooth eye movements would manifest itself only in the form of smooth pursuit but not independently from a moving object. Synchronization between a driven system and a driv- ing system is a well-known and well-investigated gen- eral phenomenon in dynamical systems [49,60]. In par- ticular, the concept of phase synchronization has been found wide applicability in physiology [21,46] and the neurosciences [61,67]. Synchronization of biological sys- tems with environmental signals has been proposed as a mechanism which may allow for real-time reactions of biological systems to predictable signals [73, 75]. In gen- eral, synchronization can be observed in coupled dissi- pative dynamical systems which possess a negative feed- back coupling. In the realm of the oculomotor system [10], negative feedback is also known as on-line gain con- trol [53, 54]. It is difficult to prove synchronization alone from ob- servations of the driving and the driven system, because in the synchronous state, in the ideal case the driven system follows the driving system exactly, and nothing can be inferred about the equations of motion of the driven system and its coupling to the driving system. But systems can be tested for synchronization by look- ing at irregular motion [13], for example after a brief perturbation [11], and then comparing the resulting dy- namics with what the equations of motion of the driven