Controlling Complex Dynamics in a Protected Area Discrete-Time Model
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 b...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/432319 |
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| _version_ | 1849414163762249728 |
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| author | Paolo Russu |
| author_facet | Paolo Russu |
| author_sort | Paolo Russu |
| collection | DOAJ |
| description | 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 (𝛽) and the defensive expenditures (𝜌𝛽) specifically directed towards at the protection of the environmental resource. We observed that some values of 𝛽 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. |
| format | Article |
| id | doaj-art-6e69b8e5604a4cf9bb6ba0ae2ecd7f79 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6e69b8e5604a4cf9bb6ba0ae2ecd7f792025-08-20T03:33:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/432319432319Controlling Complex Dynamics in a Protected Area Discrete-Time ModelPaolo Russu0Faculty of Economics, DEIR, University of Sassari, via Torre Tonda 34, 07100 Sassari, ItalyThis 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 (𝛽) and the defensive expenditures (𝜌𝛽) specifically directed towards at the protection of the environmental resource. We observed that some values of 𝛽 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.http://dx.doi.org/10.1155/2012/432319 |
| spellingShingle | Paolo Russu Controlling Complex Dynamics in a Protected Area Discrete-Time Model Discrete Dynamics in Nature and Society |
| title | Controlling Complex Dynamics in a Protected Area Discrete-Time Model |
| title_full | Controlling Complex Dynamics in a Protected Area Discrete-Time Model |
| title_fullStr | Controlling Complex Dynamics in a Protected Area Discrete-Time Model |
| title_full_unstemmed | Controlling Complex Dynamics in a Protected Area Discrete-Time Model |
| title_short | Controlling Complex Dynamics in a Protected Area Discrete-Time Model |
| title_sort | controlling complex dynamics in a protected area discrete time model |
| url | http://dx.doi.org/10.1155/2012/432319 |
| work_keys_str_mv | AT paolorussu controllingcomplexdynamicsinaprotectedareadiscretetimemodel |