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This article is cited in 10 scientific papers (total in 10 papers)
Lotka–Volterra Equations in Three Dimensions Satisfying the Kowalevski–Painlevé Property
Kyriacos Constandinides, Pantelis A. Damianou Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
Abstract:
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.
Keywords:
Lotka–Volterra equations, Kowalevski exponents, Painlevé analysis.
Received: 02.10.2010 Accepted: 22.11.2010
Citation:
Kyriacos Constandinides, Pantelis A. Damianou, “Lotka–Volterra Equations in Three Dimensions Satisfying the Kowalevski–Painlevé Property”, Regul. Chaotic Dyn., 16:3-4 (2011), 311–329
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https://www.mathnet.ru/eng/rcd440 https://www.mathnet.ru/eng/rcd/v16/i3/p311
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