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A Population Harvesting Model with Time and Size Competition Dependence Function

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Abstract

We consider a nonlinear model describing a forest harvesting of a size-structured trees population with intra-specific competition, where the population compete with trees of bigger size. Using a fixed point argument, we prove the existence of a unique solution to the problem. We also prove the existence of an optimal control where the objective functional includes the benefits from timber production. Then, we give the necessary condition of optimality for the optimal control and give its characterization as well.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux (IMB) UMR CNRS 5251, Université de Bordeaux, 351 Cours de la Libération, 33405, Talence, France

    B. Ainseba

  2. UMR EcoFoG (AgroParisTech, Cirad, CNRS, Inrae, Université des Antilles), Université de Guyane, Campus de Troubiran, 97337, Cayenne Cedex, France

    L. Louison & A. Omrane

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  1. B. Ainseba
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  2. L. Louison
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  3. A. Omrane
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Correspondence to A. Omrane.

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Communicated by Vincenzo Capasso.

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Ainseba, B., Louison, L. & Omrane, A. A Population Harvesting Model with Time and Size Competition Dependence Function. J Optim Theory Appl 195, 647–665 (2022). https://doi.org/10.1007/s10957-022-02102-2

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