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<p>In this paper, we study Hopf bifurcation for planar piecewise smooth near-Hamiltonian systems with an elementary center, and obtain some new properties of the first order Melnikov function. As an application, we give upper and lower bounds of the maximum number of limit cycles of a piecewise polynomial system near the elementary center.</p>

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On Hopf Bifurcation in Piecewise Smooth Near-Hamiltonian Systems

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Maoan Han,
  • Zening Lai

摘要

In this paper, we study Hopf bifurcation for planar piecewise smooth near-Hamiltonian systems with an elementary center, and obtain some new properties of the first order Melnikov function. As an application, we give upper and lower bounds of the maximum number of limit cycles of a piecewise polynomial system near the elementary center.