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Global Dynamics of a Whirling Pendulum System

  • Shuting Sun [1] ; Xingwu Chen [2]
    1. [1] Sichuan University

      Sichuan University

      China

    2. [2] Chongqing University of Arts and Sciences

      Chongqing University of Arts and Sciences

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper we investigate the global dynamics of a three-parametric whirling pendulum system with external force. By the comparison technology of divergence integrals and the rotation theory of vector fields, we give the complete bifurcation diagram in the whole parameter space including surfaces of Hopf bifurcation, heteroclinic and homoclinic bifurcation, double limit cycle bifurcation, as well as all global phase portraits. The main results show that the cyclicity of this system is 3 and there are plentiful orbit structures such as double-homoclinic loop, double-heteroclinic loop and different kinds of saddle connections. Final numerical simulations coincide with the theoretical results.

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