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2020 | OriginalPaper | Buchkapitel

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

verfasst von : Alexander I. Smirnov, Vladimir D. Mazurov

Erschienen in: Optimization and Applications

Verlag: Springer International Publishing

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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.

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Metadaten
Titel
Generalization of Controls Bimodality Property in the Optimal Exploitation Problem for Ecological Population with Binary Structure
verfasst von
Alexander I. Smirnov
Vladimir D. Mazurov
Copyright-Jahr
2020
DOI
https://doi.org/10.1007/978-3-030-38603-0_16