On the algebraic limit cycles of quadratic systems

• Javier Chavarriga ^[1] ; Jaume Llibre ^[2] ; Jordi Sorolla ^[1]
  1. [1] Universitat de Lleida

     Universitat de Lleida

     Lérida, España

     
  2. [2] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
• Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals , Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 509-510
• Idioma: inglés
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• Resumen

  • Four type of algebraic limit cycles for quadratic systems are known: one of degree two and three of degree four. But there is not a definitive result about the algebraic limit cycles of a quadratic system. In this paper we give a characterization of the irreducible invariant algebraic curves of fourth degree of a quadratic system containing an oval which is an algebraic limit cycle of the system, showing that there are exactly four families of algebraic limit cycles of degree 4 for quadratic systems.