This question concerns the generalized logistic function, discussed in Wikipedia here:
If we take the lower asymptote to be 0, then the upper asymptote is called the carrying capacity. Fine, and for sake of this question, let’s take the lower asymptote to be 0 (not that it matters for the mathematics of this question, but that gives us the convenient handle of “carrying capacity” to use in this question.) The problem is that in the differential form (Y’(t) = …), it appears that the rate of population growth can be increased simply by increasing the carrying capacity. In other words, the distance of the boundary of the constraint is somehow being “telegraphed” to the population. This seems counter-intuitive to me. Until the population starts to feel the effects of the constraint, a relaxing of the constraint should be imperceptible to the population. Obviously, I’m missing something, but what is it?