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Controlling Complex Dynamics in a Protected Area Discrete-Time Model

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  • Paolo Russu

Abstract

This paper investigates how the introduction of user fees and defensive expenditures changes the complex dynamics of a discrete-time model, which represents the interaction between visitors and environmental quality in an 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 ( 𠛽 ) and the defensive expenditures ( 𠜌 𠛽 ) specifically directed towards at the protection of the environmental resource. We observed that some values of 𠛽 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

  • Paolo Russu, 2012. "Controlling Complex Dynamics in a Protected Area Discrete-Time Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, March.
    • Handle: RePEc:hin:jnddns:432319
    DOI: 10.1155/2012/432319
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    Cited by:

    1. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
    2. A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.

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