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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Main Author:	Paolo Russu
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Discrete Dynamics in Nature and Society
Online Access:	http://dx.doi.org/10.1155/2012/432319

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spelling	doaj-6e69b8e5604a4cf9bb6ba0ae2ecd7f792020-11-24T22:16:29ZengHindawi LimitedDiscrete 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
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Paolo Russu
spellingShingle	Paolo Russu Controlling Complex Dynamics in a Protected Area Discrete-Time Model Discrete Dynamics in Nature and Society
author_facet	Paolo Russu
author_sort	Paolo Russu
title	Controlling Complex Dynamics in a Protected Area Discrete-Time Model
title_short	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_sort	controlling complex dynamics in a protected area discrete-time model
publisher	Hindawi Limited
series	Discrete Dynamics in Nature and Society
issn	1026-0226 1607-887X
publishDate	2012-01-01
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.
url	http://dx.doi.org/10.1155/2012/432319
work_keys_str_mv	AT paolorussu controllingcomplexdynamicsinaprotectedareadiscretetimemodel
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Controlling Complex Dynamics in a Protected Area Discrete-Time Model

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