IDEAS home Printed from https://ideas.repec.org/p/bol/bodewp/654.html
   My bibliography  Save this paper

Closed form solutions to generalized logistic-type nonautonomous systems

Author

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

Abstract

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 (?1; ?2) extension of the Appell generalized hypergeometric function, Al-Shammery and Kalla (2000); about such a extension a new analytic continuation theorem has been proved.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://amsacta.unibo.it/4592/1/654.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arantza Gorostiaga & Jana Hromcová & Miguel-Ángel López-García, 2013. "Optimal taxation in the Uzawa–Lucas model with externality in human capital," Journal of Economics, Springer, vol. 108(2), pages 111-129, March.
    2. Agustin, PEREZ BARAHONA, 2007. "Capital Accumulation and Non-Renewable Energy Resources : a Special Functions Case," Discussion Papers (ECON - Département des Sciences Economiques) 2007008, Université catholique de Louvain, Département des Sciences Economiques.
    3. Rauf, BOUCEKKINE & Blanca, MARTINEZ & Jose R., RUIZ-TAMARIT, 2007. "Global dynamics and imbalance effects in the Lucas Uzawa model : further results," Discussion Papers (ECON - Département des Sciences Economiques) 2007018, Université catholique de Louvain, Département des Sciences Economiques.
    4. Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
    5. Bofota, Youyou Baende & Boucekkine, Raouf & Bala, Alain Pholo, 2016. "Social Capital As An Engine Of Growth: Multisectoral Modeling And Implications," Macroeconomic Dynamics, Cambridge University Press, vol. 20(8), pages 2093-2122, December.
    6. Hiraguchi, Ryoji, 2009. "A solution to the Lucas-Uzawa model with increasing returns to scale: Note," Economic Modelling, Elsevier, vol. 26(5), pages 831-834, September.
    7. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas–Uzawa model," Economic Modelling, Elsevier, vol. 28(1), pages 109-117.
    8. Raouf, BOUCEKKINE & Bity, DIENE & Theophile, AZOMAHOU, 2006. "The Growth economics of epidemics," Discussion Papers (ECON - Département des Sciences Economiques) 2006021, Université catholique de Louvain, Département des Sciences Economiques.
    9. Iulia PARA & Ioana VIASU, 2018. "On the Solutions to the Ramsey Model with Logistic Population Growth via the Partial Hamiltonian Approach," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 142-150, December.
    10. Constantin Chilarescu & Ioana Viasu, 2016. "A Closed-form Solution of a Two-sector Endogenous Growth Model with Habit Formation," Australian Economic Papers, Wiley Blackwell, vol. 55(2), pages 112-127, June.
    11. Boucekkine, R. & Martínez, B. & Ruiz-Tamarit, J.R., 2013. "Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 312-334.
    12. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, "undated". "Optimal Firm Behavior under Environmental Constraints," Working Papers 2008_11, Business School - Economics, University of Glasgow.
    13. Massimiliano Marzo & Daniele Ritelli & Paolo Zagaglia, 2011. "Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method," Working Paper series 52_11, Rimini Centre for Economic Analysis.
    14. Constantin Chilarescu, 2019. "On the Solutions of the Lucas-Uzawa Model," Papers 1907.12658, arXiv.org.
    15. José Ramón Ruiz Tamarit & Manuel Sánchez Moreno, 2006. "Optimal Regulation And Growth In A Natural-Resource-Based Economy," Working Papers. Serie AD 2006-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    16. Roy Cerqueti & Raffaella Coppier & Gustavo Piga, 2012. "Corruption, growth and ethnic fractionalization: a theoretical model," Journal of Economics, Springer, vol. 106(2), pages 153-181, June.
    17. Nastasia Henry & Alain Venditti, 2023. "On the (de)stabilization role of protectionism: Theory and evidence," Working Papers hal-04311555, HAL.
    18. Benchekroun, Hassan & Withagen, Cees, 2011. "The optimal depletion of exhaustible resources: A complete characterization," Resource and Energy Economics, Elsevier, vol. 33(3), pages 612-636, September.
    19. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).
    20. Kazuyuki Sasakura, 2020. "The Education Sector and Economic Growth: A First Study of the Uzawa Model," Working Papers 2013, Waseda University, Faculty of Political Science and Economics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bol:bodewp:654. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Dipartimento Scienze Economiche, Universita' di Bologna (email available below). General contact details of provider: https://edirc.repec.org/data/sebolit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.