A differential equation model for the stage theory of color perception

We propose a novel differential equation model assuming the stage theory (trichromatic theory and opponent-process theory) for color inputs based on our previous model for light-dark inputs, which is an extension of the lateral inhibition model proposed by Peskin (Partial Differential Equations in Biology: Courant Institute of Mathematical Sciences Lecture Notes, New York, 1976). First, we consider the stationary problem in our novel model for color inputs and show that the output of our model can be described by a convolution integral. Moreover, we derive the necessary and sufficient conditions for the appearance of Mexican hat-type integral kernels in the outputs of our model for color inputs. Second, we demonstrate numerical results for simple color inputs and provide a theoretical prediction that the self-control mechanism exerted at horizontal cells, in conjunction with the opponent-colors (red-green, yellow-blue, and light-dark (or white-black)) plays an important role for the occurrence and non-occurrence of typical color contrasts.