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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 studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval.

Keywords

adjoint systembang-bang controlcost functionalPontrjagin's maximum principletransversality conditions
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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