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First Integrals of the May–Leonard Asymmetric System

Author

Listed:
  • 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
    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)

  • Natalie L. Shcheglova

    (Faculty of Mechanics and Mathematics, Belarusian State University, Nezavisimosti avenue 4, 220030 Minsk, Belarus)

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.

Suggested Citation

  • Valery Antonov & Wilker Fernandes & Valery G. Romanovski & Natalie L. Shcheglova, 2019. "First Integrals of the May–Leonard Asymmetric System," Mathematics, MDPI, vol. 7(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:292-:d:216079
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