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<p>In this paper, we consider the simultaneous bifurcation problem of limit cycles of types I and II near a double heteroclinic loop for a cylinder near-Hamiltonian system. We obtain a lower bound of the maximal number of limit cycles near the double heteroclinic loop by using four different Melnikov functions. We also study the number of limit cycles of a class of cylinder near-Hamiltonian systems as an application of our main results.</p>

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Finding Limit Cycles Near A Double Heteroclinic Loop on the Cylinder

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Meilan Cai,
  • Maoan Han

摘要

In this paper, we consider the simultaneous bifurcation problem of limit cycles of types I and II near a double heteroclinic loop for a cylinder near-Hamiltonian system. We obtain a lower bound of the maximal number of limit cycles near the double heteroclinic loop by using four different Melnikov functions. We also study the number of limit cycles of a class of cylinder near-Hamiltonian systems as an application of our main results.