Limit Cycles Produced Near a Double Homoclinic Loop in Perturbed Duffing Oscillators

• Wei Geng ^[1] ; Yun Tian ^[2] ; Lang Liu ^[2] ; Xiaolan Wu ^[2]
  1. [1] Zhejiang University of Science and Technology

     Zhejiang University of Science and Technology

     China

     
  2. [2] Shanghai Normal University

     Shanghai Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 4, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we study limit cycle bifurcations near a symmetric double homoclinic loop in planar cubic near-Hamiltonian systems by high-order analysis.We find 6 limit cycles from the exterior period annulus near the loop by the third-order Melnikov function, where a type of pseudo-Abelian integrals are involved. Furthermore, using Melnikov functions of different orders for the exterior and inner annuli respectively, we find a new distribution (6, 1, 1) for limit cycles bifurcating near the loop.

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