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Optimal pest control problem in population dynamics. (English) Zbl 1213.92067
Summary: One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the maximum principle of Pontryagin. Dynamic programming was used for the resolution of the second optimal pest control problem.

MSC:
92D40 Ecology
49N90 Applications of optimal control and differential games
90C39 Dynamic programming
34H05 Control problems involving ordinary differential equations
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