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logistic growth rate

Mathematical Modelling of Natural Phenomena (1)

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An Optimal Control Problem for a Predator-PreyReaction-Diffusion System
N. C. Apreutesei
Journal:

Mathematical Modelling of Natural Phenomena / Volume 5 / Issue 6 / 2010

Published online by Cambridge University Press:

13 September 2010, pp. 180-195

Print publication:

2010
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An optimal control problem is studied for a predator-prey system of PDE, with a logisticgrowth rate of the prey and a general functional response of the predator. The controlfunction has two components. The purpose is to maximize a mean density of the two speciesin their habitat. The existence of the optimal solution is analyzed and some necessaryoptimality conditions are established. The form of the optimal control is found in someparticular cases.