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Open AccessArticle

First Integrals of the May–Leonard Asymmetric System

Department of Mathematics, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, Russia
Departamento de Matemática e Estatística, Universidade Federal de São João del Rei, São João del Rei, Minas Gerais 36307-352, Brazil
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, Slovenia
Center for Applied Mathematics and Theoretical Physics, Mladinska 3, SI-2000 Maribor, Slovenia
Faculty of Natural Science and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
Faculty of Mechanics and Mathematics, Belarusian State University, Nezavisimosti avenue 4, 220030 Minsk, Belarus
Author to whom correspondence should be addressed.
Mathematics 2019, 7(3), 292;
Received: 8 January 2019 / Revised: 10 March 2019 / Accepted: 15 March 2019 / Published: 21 March 2019
(This article belongs to the Special Issue Computer Algebra in Scientific Computing)
PDF [267 KB, uploaded 21 March 2019]


For the May–Leonard asymmetric system, which is a quadratic system of the Lotka–Volterra type depending on six parameters, we first look for subfamilies admitting invariant algebraic surfaces of degree two. Then for some such subfamilies we construct first integrals of the Darboux type, identifying the systems with one first integral or with two independent first integrals. View Full-Text
Keywords: integrability; invariant surfaces; Lotka–Volterra system; computational algebra integrability; invariant surfaces; Lotka–Volterra system; computational algebra
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Antonov, V.; Fernandes, W.; Romanovski, V.G.; Shcheglova, N.L. First Integrals of the May–Leonard Asymmetric System. Mathematics 2019, 7, 292.

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