Closed form solutions to generalized logistic-type nonautonomous systems

Abstract

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 logis- tically on its own. In such a way we get again the model of (10), numer- ically 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 in- dependent logistic dynamics. The population dynamics is then found in closed form through a more di-cult integration, involving a (?1;?2) exten- sion of the Appell generalized hypergeometric function, (2); a new analytic continuation theorem has been proved about such an extension.