On Double Homoclinic Bifurcation of Limit Cycles in Near-Hamiltonian Systems on the Cylinder

• Ai Ke ^[1] ; Junmin Yang ^[2]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

     
  2. [2] Hebei Normal University

     Hebei Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
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• Resumen

  • We study the bifurcation problem of limit cycles in near-Hamiltonian systems near a double homoclinic loop on the cylinder. We obtain a sufficient condition to find a lower bound of the maximal number of limit cycles near the loop by the coefficients of the expansions of the three Melnikov functions corresponding to the three families of periodic orbits near the double homoclinic loop. We also provide an application of our main results to a class of cylindrical systems.