This investigation examined a three-component differential equation model with a self-control mechanism in vision, proposed as a slight extension of the 1976 C. S. Peskin's lateral inhibition model, by analyzing the input signal I = I(t, x) depending on time t and position x ∈ R. Investigations revealed that a solution could be represented in the convolution integral form and that T > 0 existed such that the integral kernel Kp(t, x) was positive for x ∈ R and t ∈ (0, T ). We also numerically demonstrated from experimental neurophysiological observations that Kp(t, x) includes the Mexican-hat function and the temporal biphasic function under certain conditions, and there was a time lag before the Mexican-hat function appeared in Kp(t, x). We also numerically predicted that an asymmetrical temporal response in the self-control mechanism plays a vital role in obtaining visual impressions for afterimage rotations.