IJPAM: Volume 78, No. 1 (2012)

ON THE OPTIMALITY OF LIMIT CYCLES
IN NATURE BASED-TOURISM

Paolo Russu
Department of Economics
Business and Regulation
University of Sassari
34, via Torre Tonda, 07100, Sassari, ITALY


Abstract. Virgin nature, as well as historical and cultural monuments located in National Parks, all form part of our national heritage. Tourism and recreation allow visitors to National Parks to enjoy nature, to reinstate, recover and broaden their personal outlook, to experience local history, culture, flora and fauna and to interact with the environment harmoniously. One of the objectives of the administration of a Governmental Institution 'National Park' is to maximize profits from tourism and recreation, where profit is defined as the difference between the revenues from visitors and the sum of expenditures on recreation investments and defensive expenditures for ensuring the preservation of natural and cultural heritage. This paper is an attempt to model some relevant aspects of these prey-predator relations. The model is formulated in terms of optimal control theory, and then is transformed into an `augmented' dynamic system by meas of the optimal choice of control variables resulting form the application of Pontryagin's Maximum Principle. It turns out that, for reasonable parameter values, the optimal trajectory exhibits a cyclical behavior.

Received: January 4, 2012

AMS Subject Classification:

Key Words and Phrases: bioeconomic model, tourism, optimal dynamic control model, optimal policy mix, financing and protected areas

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 1