First Integrals of the May–Leonard Asymmetric System

Valery Antonov, Wilker Fernandes, Valery G. Romanovski and Natalie L. Shcheglova
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Valery Antonov: Department of Mathematics, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, Russia
Wilker Fernandes: Departamento de Matemática e Estatística, Universidade Federal de São João del Rei, São João del Rei, Minas Gerais 36307-352, Brazil
Valery G. Romanovski: Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, Slovenia
Natalie L. Shcheglova: Faculty of Mechanics and Mathematics, Belarusian State University, Nezavisimosti avenue 4, 220030 Minsk, Belarus

Mathematics, 2019, vol. 7, issue 3, 1-15

Abstract: 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.

Keywords: integrability; invariant surfaces; Lotka–Volterra system; computational algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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