Closed form solutions to generalized logistic-type nonautonomous systems - Giovanni Mingari Scarpello; Arsen Palestini; Daniele Ritelli (Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), 2009)
In this paper the subject is met of providing a two-fold generalization of the logistic popu- lation 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 Meyer and Ausubel (1999), by them computed numerically, and we solve it completely through the Gauss hypergeometric function. Furthermore, both the carrying ca- pacity and net growth rate are assumed to change simultaneously following two independent logisticals. The population dynamics is then found in closed form through a more difficult integration, involving a (τ1; τ2) extension of the Appell generalized hypergeometric function, Al-Shammery and Kalla (2000); about such a extension a new analytic continuation theorem has been proved.
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