Math. Model. Nat. Phenom.
Volume 1, Number 1, 2006Population dynamics
|Page(s)||120 - 132|
|Published online||15 May 2008|
Necessary Optimality Conditions for a Lotka-Volterra Three Species System
Department of Mathematics, Technical University “Gh.
Asachi”, 700506, Iasi, Romania
Corresponding author: email@example.com
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.
Mathematics Subject Classification: 34H05 / 49K15 / 49J15 / 92B05 / 93C15
Key words: adjoint system / bang-bang control / cost functional / Pontrjagin's maximum principle / transversality conditions
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