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Closed form solutions to generalized logistic-type nonautonomous systems


  • G. Mingari Scarpello
  • A. Palestini
  • D. Ritelli


In this paper the subject is met of providing 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 Meyer and Ausubel (1999), by them computed numerically, 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 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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  • G. Mingari Scarpello & A. Palestini & D. Ritelli, 2009. "Closed form solutions to generalized logistic-type nonautonomous systems," Working Papers 654, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:654

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    1. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
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