IJPAM: Volume 72, No. 1 (2011)
GROWTH AND SPECIES CONSERVATION
Department of Mathematics
Universidad del Valle
Calle 13, No. 100-00, Cali, COLOMBIA
Abstract. This paper proposes a bioeconomic model destined to show how the human activity may alter the natural evolution of biological species. The model is formulated in term of optimal control theory, and then is transformed into ``augmented" dynamic system by meas of the optimal choice of control variables resulting form the application of Pontryagin's maximum principle. In the case of species abundance, we prove that saddle-point stability of the original bioeconomic system is transferred to the ``augmented" system under optimal choice of control variables.
Received: June 16, 2011
AMS Subject Classification: 92D25, 49K15
Key Words and Phrases: Gompertz population growth, bioeconomic model, Pontryagin maximum principle, saddle-point stability
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395