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.
MSC Classification: 35A08 , 35K08 , 35K57 , 44A35