title: A nonlinear integral equation for visual impedance.
abstract: The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation.
mesh_terms: D006801:Humans; D008433:Mathematics; D008959:Models, Neurological; D009433:Neural Inhibition; D012684:Sensory Thresholds; D014785:Vision, Ocular / Q000502:physiology*