title: A model for dysfunctions in smooth pursuit eye movement.
abstract: In this paper, I have introduced and solved a simple deterministic model of eye tracking that produces rich dynamical behavior. Some of its main features, notably the existence of a chaotic regime, are reminiscent of the anomalies reported in smooth pursuit eye tracking experiments with schizophrenia patients. By obtaining the state diagram of such a model as a function of target frequency and amplitude, we showed the existence of a chaotic regime characterized by a strange attractor in phase-space and associated random velocity arrests in the eye dynamics. Moreover, the power spectrum contains features similar to those reported in the literature. The correctness of this model could in principle be determined by performing experiments where the target parameters (i.e., amplitude and frequency) could be varied in a systematic manner and by taking Poincaré maps from the corresponding time series. Although the present status of such experiments prevents us from verifying the validity of the model, the available data does not seem to contradict the main predictions. Furthermore, we showed that the inevitable noise expected to be present in actual experiments would only enhance the observability of our predictions. If this model were proven incorrect, then the focus of research into mechanisms will have to shift into a search for an intrinsic source of the fluctuations. If, on the other hand, this deterministic theory has any validity, it will point to the nonlinearities in eye tracking mechanisms as the main culprits for the observed anomalies.
mesh_terms: D005133:Eye Movements; D006801:Humans; D008959:Models, Neurological; D011698:Pursuit, Smooth; D012559:Schizophrenia / Q000503:physiopathology*