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A Population Harvesting Model with Time and Size Competition Dependence Function

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Listed:
  • B. Ainseba

    (Université de Bordeaux)

  • L. Louison

    (Université de Guyane)

  • A. Omrane

    (Université de Guyane)

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.

Suggested Citation

  • B. Ainseba & L. Louison & A. Omrane, 2022. "A Population Harvesting Model with Time and Size Competition Dependence Function," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 647-665, November.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02102-2
    DOI: 10.1007/s10957-022-02102-2
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    References listed on IDEAS

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    1. Nobuyuki Kato & Hiroyuki Torikata, 1997. "Local existence for a general model of size-dependent population dynamics," Abstract and Applied Analysis, Hindawi, vol. 2, pages 1-20, January.
    2. B. Skritek & V. M. Veliov, 2015. "On the Infinite-Horizon Optimal Control of Age-Structured Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 243-271, October.
    3. Goetz, Renan Ulrich & Hritonenko, Natali & Mur, Ruben & Xabadia, Àngels & Yatsenko, Yuri, 2013. "Forest management for timber and carbon sequestration in the presence of climate change: The case of Pinus Sylvestris," Ecological Economics, Elsevier, vol. 88(C), pages 86-96.
    4. Olli Tahvonen, 2004. "Optimal Harvesting Of Forest Age Classes: A Survey Of Some Recent Results," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 205-232.
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