Darboux polynomials for Lotka-Volterra systems in three dimensions
Mathematical Physics
2015-05-13 v1 Classical Analysis and ODEs
math.MP
Abstract
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.
Cite
@article{arxiv.0810.3103,
title = {Darboux polynomials for Lotka-Volterra systems in three dimensions},
author = {Yiannis T. Christodoulides and Pantelis A. Damianou},
journal= {arXiv preprint arXiv:0810.3103},
year = {2015}
}
Comments
16 pages