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Application of Singular Space-Time Transformation to Impulsive Pest Management

Авторы: Goncharova E.V., Staritsyn M.V.

Журнал: Cybernetics and Physics

Том: 4

Номер: 2

Год: 2015

Отчётный год: 2015

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Аннотация: We consider three versions of a problem of impulsive pest control by its natural enemies. The model is of a prey-predator type. The control system is described by a measure differential equation and hence admits discontinuous solutions. The cost functional of the first problem represents a balance between a negative profit provided by a pest (prey) and a price for applying an additional population of its natural enemies (predators). The problem of keeping the pest quantity below a practically admissible threshold leads to a state-constrained model, while the most complicated version is due to the presence of a mixed constraint relating impulsive action (measure) and the left one-sided limit of a trajectory. We employ a conceptual approach for optimal impulsive pest control based on a certain singular space-time transformation and share our experience in its numerical implementation.

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