Adaptation is the eventual restoration of the level despite the lasting presence of a change in a stimulus that temporarily caused a change in the read out. The incoherent feed-forward loop is one way to use three nodes to produce this effect. After the level of input A rises, activation of read out C rises, but inhibition of C through B also rises. The final steady-state level of read out C is unchanged. However, since the level of inhibitor B takes some time to rise, inhibition of C is temporarily insufficient to compensate for increased activation of C by A. Thus, the level of C is temporarily higher before it approaches its original value.
We visualize nullclines and critical points in the BC phase portrait before and after a step change in A.
