Bifurcation of Limit Cycles in a Class of Piecewise Smooth Cubic Rayleigh-Liénard Systems

• Fang Wu ^[1] ; Ting Chen ^[1] ; Xin Li ^[1]
  1. [1] National University of Defense Technology

     National University of Defense Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
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• Resumen

  • In this paper, we investigate the classical problem related to bifurcation of smallamplitude limit cycles in a class of piecewise smooth cubic Rayleigh-Liénard systems.

    By using the developed Poincaré-Lyapunov method, we achieve the classifications of the center at the origin of such piecewise smooth polynomial system. We further provide the necessary and sufficient conditions of the global center. Furthermore, we establish that lower bound on the maximum number of limit cycles bifurcating from the origin is 5.