Closed form solutions to generalized logistic-type nonautonomous systems

This paper provides a two-fold generalization of the logistic population dynamics to a nonautonomous context. First it is assumed the carrying capacity alone pulses the population behavior changing logistically on its own. In such a way we get again the model of P. S. Meyer and J. H. Ausubel, "Carrying capacity: a model with logistically varying limits", Technological Forecasting and Social Change, 61 (1999), 209-214, numerically computed by them, and we solve it completely through the Gauss hypergeometric function. Furthermore, both the carrying capacity and net growth rate are assumed to change simultaneously following two independent logistic dynamics. The population dynamics is then found in closed form through a more difficult integration, involving a $(tau_1 ,tau_2)$ extension of the Appell generalized hypergeometric function, cite{ak}; a new analytic continuation theorem has been proved about such an extension.