Feedback on the competence
The following equation describes a possible feedback of the pattern-forming system on the ability to perform the pattern-forming reaction:
The source density (blue) has to have a much shallower distribution then the activator (green). Therefore, the coupling is achieved by a diffusible substance of a very long time constant (that may control more stable processes like gene activation). Since in such a system the activator concentration is in a wide range independent of the source density, the activator concentration remains stable although the source density increases, i.e., the system obtains a stable steady state.
An alternative is that the inhibitor with is shallower slope controls the source density.
Such an interaction would make a separate mediator for the long-range influence of the patterning system on the competence superfluous. However, since the inhibitor concentration depends on the source density, the factor 1/rho is necessary to avoid instability. Moreover, the slope of the competence cannot become steeper than that of the inhibitor, which is less effective in suppressing secondary maxima. Therefore, the simulations on the preceding page have been done with the first three equations given above.