Theory of the response of the limulus retina to periodic excitation

Abstract

Analytical and numerical solutions are given for several problems which arise from a mathematical description of inhibitory interactions in the Limulus retina. The theory developed here takes into account the delay in lateral inhibition and the gradual decay of lateral and self-inhibition. Emphasis is laid on the calculation of responses to excitation fields which are periodic in time and either spatially uniform or of traveling wave type. The analytical solutions given are intended to help experimenters determine the range in which certain linearized equations and reduced measures of excitation are useful for the design and interpretation of experiments. Certain of the numerical solutions obtained describe intrinsically non-linear effects, such as "periodic bursting" under constant excitation.