Darboux polynomials for lotkavolterra systems in three dimensions
Date
2009ISSN
1402-9251Source
Journal of Nonlinear Mathematical PhysicsVolume
16Issue
3Pages
339-354Google Scholar check
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We consider LotkaVolterra 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. © 2009 The Author(s).