IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/36599.html
   My bibliography  Save this paper

On the Optimality of Limit Cycles in Nature Based-Tourism

Author

Listed:
  • Russu, Paolo

Abstract

Virgin nature, as well as historical and cultural monuments located in National Parks, all form part of our national heritage. Tourism and recre- ation allow visitors to National Parks to enjoy nature, to reinstate, recover and broaden their personal outlook, to experience local history, culture, ora and fauna and to interact with the environment harmoniously. One of the ob- jectives of the administration of a Governmental Institution 'National Park' is to maximize prots from tourism and recreation, where prot is dened as the difference between the revenues from visitors and the sum of expenditures on recreation investments and defensive expenditures for ensuring the preserva- tion of natural and cultural heritage. This paper is an attempt to model some relevant aspects of these prey-predator relations. The model is formulated in terms of optimal control theory, and then is transformed into an `augmented' dynamic system by meas of the optimal choice of control variables resulting form the application of Pontryagin's Maximum Principle. It turns out that, for reasonable parameter values, the optimal trajectory exhibits a cyclical behavior.

Suggested Citation

  • Russu, Paolo, 2012. "On the Optimality of Limit Cycles in Nature Based-Tourism," MPRA Paper 36599, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:36599
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/36599/1/MPRA_paper_36599.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Barbier, Edward B. & Schulz, Carl-Erik, 1997. "Wildlife, biodiversity and trade," Environment and Development Economics, Cambridge University Press, vol. 2(2), pages 145-172, May.
    2. Kerkvliet, Joe & Nowell, Clifford, 2000. "Tools for recreation management in parks: the case of the greater Yellowstone's blue-ribbon fishery," Ecological Economics, Elsevier, vol. 34(1), pages 89-100, July.
    3. Li, Chuan-Zhong & Löfgren, Karl-Gustaf, 1998. "A dynamic model of biodiversity preservation," Environment and Development Economics, Cambridge University Press, vol. 3(2), pages 157-172, May.
    4. G. Feichtinger & R. F. Hartl & P. M. Kort & A. J. Novak, 2001. "Terrorism Control in the Tourism Industry," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 283-296, February.
    5. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," MPRA Paper 34397, University Library of Munich, Germany.
    6. Engelbert Dockner & Gustav Feichtinger, 1991. "On the optimality of limit cycles in dynamic economic systems," Journal of Economics, Springer, vol. 53(1), pages 31-50, February.
    7. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kaslik, Eva & Neamţu, Mihaela, 2020. "Dynamics of a tourism sustainability model with distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

    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. Simone Borghesi & Angelo Antoci & Paolo Russu, 2004. "Biodiversity and Economic Growth: Stabilization Versus Preservation of the Ecological Dynamics," Working Papers 2004.18, Fondazione Eni Enrico Mattei.
    2. Russu, Paolo, 2011. "Controlling complex dynamics in a protected-area discrete-time model," MPRA Paper 36598, University Library of Munich, Germany.
    3. Kaslik, Eva & Neamţu, Mihaela, 2020. "Dynamics of a tourism sustainability model with distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Alfred Greiner, 2004. "Global warming in a basic endogenous growth model," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 6(1), pages 49-73, March.
    5. A. Prskawetz, 1998. "Government Debt, Budget Surplus, and Popularity of Politicians," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 131-149, July.
    6. Chenavaz, Régis Y. & Leocata, Marta & Ogonowska, Malgorzata & Torre, Dominique, 2022. "Sustainable tourism," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    7. Greiner, Alfred & Feichtinger, Gustav & Haunschmied, Josef L. & Kort, Peter M. & Hartl, Richard F., 2001. "Optimal periodic development of a pollution generating tourism industry," European Journal of Operational Research, Elsevier, vol. 134(3), pages 582-591, November.
    8. Barbier, E. & Bulte, E.H., 2004. "Introduction to the symposium on trade, renewable resources and biodiversity," Other publications TiSEM 23d4672f-7b59-47f8-b81e-c, Tilburg University, School of Economics and Management.
    9. Polasky, Stephen & Costello, Christopher & McAusland, Carol, 2004. "On trade, land-use, and biodiversity," Journal of Environmental Economics and Management, Elsevier, vol. 48(2), pages 911-925, September.
    10. Carole Ropars-Collet & Philippe Goffe & Qods Lefnatsa, 2021. "Does catch-and-release increase the recreational value of rivers? The case of salmon fishing," Review of Agricultural, Food and Environmental Studies, Springer, vol. 102(4), pages 393-424, December.
    11. Song, Haiyan & Gartner, William C. & Tasci, Asli D.A., 2012. "Visa restrictions and their adverse economic and marketing implications – Evidence from China," Tourism Management, Elsevier, vol. 33(2), pages 397-412.
    12. Bulte, E.H. & Barbier, E., 2005. "Trade and renewable resources in a second best world : An overview," Other publications TiSEM b32c301d-ca5d-47bb-ae5a-7, Tilburg University, School of Economics and Management.
    13. William A. Barnett & Yijun He & ., 1999. "Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really were Keynesian?," Macroeconomics 9906008, University Library of Munich, Germany.
    14. Philippe Le Goffe & Julien Salanie, 2004. "Recreational fishing in France : Market or institutional failures ?," Post-Print hal-02338173, HAL.
    15. Wirl, Franz, 2002. "Stability and limit cycles in competitive equilibria subject to adjustment costs and dynamic spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 26(3), pages 375-398, March.
    16. Francisco Cabo & Guiomar Martín-Herrán, 2006. "North–South transfers vs biodiversity conservation: a trade differential game," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 40(2), pages 249-278, June.
    17. Eichner, Thomas & Pethig, Rüdiger, 2016. "Coaseian biodiversity conservation. Who benefits?," VfS Annual Conference 2016 (Augsburg): Demographic Change 145745, Verein für Socialpolitik / German Economic Association.
    18. Gaowang Wang & Heng-fu Zou, 2010. "Multiple Equilibria and Indeterminacy in an Optimal Growth Model with Endogenous Capital Depreciation," CEMA Working Papers 392, China Economics and Management Academy, Central University of Finance and Economics.
    19. Naoto Jinji, 2006. "International trade and terrestrial open-access renewable resources in a small open economy," Canadian Journal of Economics, Canadian Economics Association, vol. 39(3), pages 790-808, August.
    20. Matsumoto, Akio, 1998. "Non-linear structure of a Metzlerian inventory cycle model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 481-492, January.

    More about this item

    Keywords

    bioeconomic model; tourism; optimal dynamic control model; optimal policy mix; financing and protected areas;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:36599. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.