A Polynomial System of Degree Four with an Invariant Square Containing At Least Five Limit Cycles

• Maite Grau ^[1] ; Iván Szántó ^[2]
  1. [1] Universitat de Lleida

     Universitat de Lleida

     Lérida, España

     
  2. [2] Universidad Técnica Federico Santa María
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We consider a class of polynomial systems of degree four with four real invariant straight lines that form a square, called this an invariant square, and also that contains in its interior at least five small amplitude limit cycles for a certain choice of the parameters. Moreover, we will obtain the necessary and sufficient conditions for the critical point inside the square to be a center.

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