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The Resonant Center Problem for a 2:-3 Resonant Cubic Lotka–Volterra System

  • Jaume Giné
  • Colin Christopher
  • Mateja Prešern
  • Valery G. Romanovski
  • Natalie L. Shcheglova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)

Abstract

Using tools of computer algebra we derive the conditions for the cubic Lotka–Volterra system \(\dot x = x( 2 - a_{20} x^2 - a_{11} xy - a_{02} y^2)\), \(\dot y = y(-3 + b_{20} x^2 + b_{11} xy + b_{02} y^2)\) to be linearizable and to admit a first integral of the form Φ(x,y) = x 3 y 2 + ⋯ in a neighborhood of the origin, in which case the origin is called a 2: − 3 resonant center.

Keywords

resonant center problem polynomial systems of differential equations first integral 

1991 Mathematics Subject classification

Primary 34C14 Secondary 34A26 37C27 34C25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jaume Giné
    • 1
  • Colin Christopher
    • 2
  • Mateja Prešern
    • 3
  • Valery G. Romanovski
    • 4
    • 5
  • Natalie L. Shcheglova
    • 6
  1. 1.Departament de MatemàticaUniversitat de LleidaLleidaSpain
  2. 2.School of Computing and MathematicsPlymouth UniversityPlymouthUK
  3. 3.Department of Mathematics and StatisticsUniversity of StrathclydeGlasgowUnited Kingdom
  4. 4.CAMTP - Center for Applied Mathematics and Theoretical PhysicsUniversity of MariborMariborSlovenia
  5. 5.Faculty of Natural Science and MathematicsUniversity of MariborMariborSlovenia
  6. 6.Faculty of Mechanics and MathematicsBelarusian State UniversityMinskBelarus

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