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On the Optimality of Limit Cycles in Nature Based-Tourism

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/36599/1/MPRA_paper_36599.pdf
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    References listed on IDEAS

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    1. 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.
    2. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," MPRA Paper 34397, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. 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.
    6. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.
    7. 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.
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    Cited by:

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

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    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

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