A model for light adaptation: producing Weber's law with bleaching-type kinetics

An "adaptation model" having two stages is introduced and its mathematical properties are examined. The two stages are the "adaptive process" (parameter Kb), which has bleaching-type kinetics, and the "response function" (parameters Kr and n), which incorporates response saturation. In order to study the increment threshold functions generated by the "adaptation model" the concept of a "detector" is required. It is demonstrated that without an adaptive process the compression hypothesis, in the form of the "difference equation", produces increment threshold functions which saturate and do not obey Weber's law. It is then shown that an adaptive process with bleaching-type kinetics can prevent saturation and produce Weber's law behavior provided that the "adaptive strength" of the system exceeds the "detector sensitivity".