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Necessary conditions for the existence of quasi-polynomial invariants: The quasi-polynomial and Lotka-Volterra systems

par Figueiredo, Annibal;Rocha Filho, Tarcísio T.M.;Brenig, Léon
Référence Physica. A, 262, 1-2, page (158-180)
Publication Publié, 1999

Article révisé par les pairs

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Résumé :

We show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka-Volterra dynamical system. We show how this quasi-polynomial invariant can be decomposed in a simple manner. This decomposition permits to conclude that the existence of polynomial semi-invariants in Lotka-Volterra systems is a necessary condition for the existence of quasi-polynomial invariants. We derive a method which allows to construct the necessary conditions for existence of semi-invariants on Lotka-Volterra dynamical systems. Applications are given. © 1999 Elsevier Science B.V. All rights reserved.