Carrying capacity: A model with logistically varying limits.

We introduce an extension to the widely-used logistic model of growth to a limit that in turn allows for a sigmoidally increasing carrying capacity, that is, the invention and diffusion of technologies which lift the limit. We study the effect of this dynamic carrying capacity on the trajectories of simple growth models, and we use the new model to re-analyze two actual cases of the growth of human populations. English and Japanese examples with two pulses, or one change in limit, appear to verify the model. (Author's abstract)