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<p>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,&#xa0;1,&#xa0;1) for limit cycles bifurcating near the loop.</p>

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

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Wei Geng,
  • Yun Tian,
  • Lang Liu,
  • Xiaolan Wu

摘要

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.