Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 432319, 13 pages
Research Article

Controlling Complex Dynamics in a Protected Area Discrete-Time Model

Faculty of Economics, DEIR, University of Sassari, via Torre Tonda 34, 07100 Sassari, Italy

Received 5 October 2011; Accepted 4 January 2012

Academic Editor: Baodong Zheng

Copyright © 2012 Paolo Russu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 ( 𝜌 𝛽 ) 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.