Controlling complex dynamics in a protected area discrete-time model (Q444257)

Summary: We investigate 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 (\(\beta\)) and the defensive expenditures (\(\rho \beta\)) specifically directed towards at the protection of the environmental resource. We observed that some values of \(\beta\) 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.