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Generalization of Controls Bimodality Property in the Optimal Exploitation Problem for Ecological Population with Binary Structure

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Optimization and Applications (OPTIMA 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1145))

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Abstract

The problem of optimal exploitation of an ecological population with a binary structure is considered (there is an additional criterion for population structuring in addition to age or developmental stage). It is assumed that population state dynamics is described by a nonlinear generalization of the Leslie model. We prove a criterion for the existence of so-called quasi-preserving controls that support the sustainable population dynamics. Moreover, optimal quasi-preserving controls with a minimum number of nonzero coordinates (i.e., controls that preserve unchanged the largest number of structural units of a population) are found explicitly. The proposition about the minimum possible number of nonzero coordinates for optimal vectors is also proved. This proposition is a generalization to the case of a binary population structure of well-known bimodality property of optimal strategies for populations with one-dimensional structure.

This research was funded by RFBR, grant no. 19-07-01243.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russia

    Alexander I. Smirnov & Vladimir D. Mazurov

Authors
  1. Alexander I. Smirnov
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  2. Vladimir D. Mazurov
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Correspondence to Alexander I. Smirnov .

Editor information

Editors and Affiliations

  1. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  2. Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

  4. FRC CSC RAS, Moscow, Russia

    Mikhail Posypkin

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Smirnov, A.I., Mazurov, V.D. (2020). Generalization of Controls Bimodality Property in the Optimal Exploitation Problem for Ecological Population with Binary Structure. In: Jaćimović, M., Khachay, M., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2019. Communications in Computer and Information Science, vol 1145. Springer, Cham. https://doi.org/10.1007/978-3-030-38603-0_16

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  • DOI: https://doi.org/10.1007/978-3-030-38603-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38602-3

  • Online ISBN: 978-3-030-38603-0

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