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Necessary Optimality Conditions for a Lotka-Volterra Three Species System

Published online by Cambridge University Press:  15 May 2008

N. C. Apreutesei
N. C. Apreutesei*
Affiliation:
Department of Mathematics, Technical University “Gh. Asachi”, 700506, Iasi, Romania
*
napreut@net89mail.dntis.ro
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Abstract

An optimal control problem is studiedfor a Lotka-Volterra system of three differential equations. Itmodels an ecosystem of three species which coexist. The speciesare supposed to be separated from each others. Mathematically,this is modeled with the aid of two control variables. Somenecessary conditions of optimality are found in order to maximizethe total number of individuals at the end of a given timeinterval.

Keywords

adjoint systembang-bang controlcostfunctionalPontrjagin's maximum principletransversalityconditions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 1 , Issue 1: Population dynamics , 2006 , pp. 120 - 132
Copyright
© EDP Sciences, 2006

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