Lotka–Volterra Equations in Three Dimensions Satisfying the Kowalevski–Painlevé Property

We examine a class of Lotka–Volterra equations in three dimensions which satisfy the Kowalevski–Painlevé property. 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 Painlevé analysis and more specifically by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives necessary conditions. We also show that the conditions are sufficient.