Bifurcation of Limit Cycles through Perturbing a Cubic Isochronous Center in Piecewise Polynomial Differential Systems

• Xiuli Cen ^[1] ; Shangming Chen ^[1] ; Zhe Zhang ^[1]
  1. [1] Central South University

     Central South University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 6, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In the present paper, we investigate the maximum number of limit cycles bifurcating from the period annulus of a cubic isochronous center when it is perturbed by piecewise polynomials of arbitrary degree n with the switching line x = 0. By analyzing the number of zeros of the first order Melnikov function with a new Chebyshev criterion in [3], we show that the sharp upper bound on the number of limit cycles for the perturbed systems is 2n + 1 for n ≥ 1.

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