  Biological responses often obey Weber's law, according to which the magnitude
of the response depends only on the fold change in the external input. In this
study, we demonstrate that a system involving a simple autocatalytic reaction
shows such response when a chemical is slowly synthesized by the reaction from
a faster influx process. We also show that an autocatalytic reaction process
occurring in series or in parallel can obey Weber's law with an oscillatory
adaptive response. Considering the simplicity and ubiquity of the autocatalytic
process, our proposed mechanism is thought to be commonly observed in
biological reactions.
