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<p>This paper deals with the number of limit cycles for a kind of cubic Hamiltonian systems with a cuspidal loop under piecewise smooth perturbations. Based on the asymptotic expansions of the generators of the first order Melnikov function <i>M</i>(<i>h</i>), the asymptotic expansion of <i>M</i>(<i>h</i>) is derived, and then the upper and lower bounds of the number of limit cycles are obtained.</p>

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Bifurcation of Limit Cycles for a Class of Piecewise Smooth Near-Hamiltonian Systems

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Rong Wang,
  • Jihua Yang

摘要

This paper deals with the number of limit cycles for a kind of cubic Hamiltonian systems with a cuspidal loop under piecewise smooth perturbations. Based on the asymptotic expansions of the generators of the first order Melnikov function M(h), the asymptotic expansion of M(h) is derived, and then the upper and lower bounds of the number of limit cycles are obtained.