Darboux polynomials for Lotka-Volterra systems in three dimensions

Details Darboux polynomials for Lotka-Volterra systems in three dimensions Darboux polynomials for Lotka-Volterra systems in three dimensions

2008-10-17

arxiv.org/abs/0810.3103v1

Physics

Mathematical Physics

16 pages

Scientific paper

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.

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