Coexistence of Analytic and Piecewise Analytic Limit Cycles in Planar Piecewise Quadratic Differential Systems

• Leonardo P. C. da Cruz ^[1] ; Alex C. Rezende ^[2] ; Joan Torregrosa ^[3]
  1. [1] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
  2. [2] Universidade Federal de São Carlos

     Universidade Federal de São Carlos

     Brasil

     
  3. [3] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
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• Resumen

  • We study the simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems separated by a straight line. These limit cycles arise from a degenerate Hopf bifurcation at two equilibrium points in the positive and negative half-planes, as well as from an equilibrium on the separation line. All the limit cycles are of small amplitude. This bifurcation creates a configuration of limit cycles of type (3, 5, 3).

    Additionally, in each half-plane, the maximum number of small-amplitude hyperbolic limit cycles that a quadratic vector field can have is three.