Algebraic Integrability of Lotka-Volterra equations in three dimensions

Details Algebraic Integrability of Lotka-Volterra equations in three dimensions Algebraic Integrability of Lotka-Volterra equations in three dimensions

2009-09-19

arxiv.org/abs/0909.3567v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

We examine the algebraic complete integrability of Lotka-Volterra equations in three dimensions. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems. The classification is obtained using Painleve analysis and more specifically by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives necessary conditions for the algebraic integrability of the corresponding systems. We also show that the conditions are sufficient.

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