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Instability and Bifurcation Phenomena in the Hide-Skeldon-Acheson Model: a Qualitative Approach

  • Shuangling Yang [1] ; Xinxin Liu [2]
    1. [1] Sichuan Normal University

      Sichuan Normal University

      China

    2. [2] Wenzhou University of Technology
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The Hide-Skeldon-Acheson (HSA) model is a simplified representation of selfexciting dynamos for understanding the generation mechanism of magnetic fields in celestial bodies and the Earth, crucial for geophysical and astrophysical processes.

      In this paper, we analyze the bifurcation structures and instability mechanisms of the HSA model using tools from the qualitative theory of dynamical systems. We identify and classify various and rich bifurcations near equilibrium points, including pitchfork, Hopf, degenerate Hopf bifurcations, and Bogdanov-Takens bifurcations of codimension two, as well as homoclinic loop bifurcations. Additionally, we investigate the HSA model’s dynamics at infinity, revealing a global bifurcation phenomenon at infinity through a (local) saddle-node bifurcation. The physical interpretation of our analytic results is also discussed. These results provide new insights into the stability transitions and the underlying dynamical mechanisms governing the HSA model.

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