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Controlling complex dynamics in a protected-area discrete-time model

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  • Russu, Paolo

Abstract

This paper investigates how the introduction of user fees and defensive expenditures change the complex dynamics of a discrete-time model, which represents the interaction between visitors and environmental quality in a Open-Access Protected-Area (OAPA). To investigate this issue more deeply, we begin by studying in great detail the OAPA model and then we introduce the user fee () and the defensive expenditures () specifically directed towards at the protection of the environmental resource. We observed that some values of can generate a chaotic regime from a stable dynamic of the OAPA model. Finally, to eliminate the chaotic regime, we design a controller by OGY method, assuming the user fee as a controller parameter.

Suggested Citation

  • Russu, Paolo, 2011. "Controlling complex dynamics in a protected-area discrete-time model," MPRA Paper 36598, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:36598
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    References listed on IDEAS

    as
    1. Antoci, Angelo & Borghesi, Simone & Russu, Paolo, 2004. "Biodiversity and economic growth: stabilization versus preservation of the ecological dynamics," MPRA Paper 13666, University Library of Munich, Germany.
    2. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," MPRA Paper 34397, University Library of Munich, Germany.
    3. Vivaldo M. Mendes & Diana A. Mendes, 2007. "Controlling Endogenous Cycles in an OLG Economy by the OGY Method," Working Papers Series 1 ercwp0808, ISCTE-IUL, Business Research Unit (BRU-IUL).
    4. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.
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    Cited by:

    1. Russu, Paolo, 2012. "On the Optimality of Limit Cycles in Nature Based-Tourism," MPRA Paper 36599, University Library of Munich, Germany.

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    More about this item

    Keywords

    sustainable tourism; controlling chaos;

    JEL classification:

    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development

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