Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

• Jaume Llibre ^[1] ; Bruno D. Lopes ^[1] ; Jaime R. De Moraes ^[2]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
  2. [2] Universidade Estadual Paulista (Brasil)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 1, 2014, págs. 129-148
• Idioma: inglés
• DOI: 10.1007/s12346-014-0109-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers x˙ = y(−1 + 2αx + 2βx2), y˙ = x + α(y2 − x2) + 2βxy2, α ∈ R,β< 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order.