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<p>This paper estimates the number of limit cycles that bifurcate from periodic orbits of quasi-homogeneous centers under perturbations within the class of piecewise smooth polynomial systems of degree <i>n</i>. Using the first-order averaging method, we establish upper bounds for the number of limit cycles emerging from the period annuluses. As an application, the limit cycle bifurcation is studied for a quasi-homogeneous Hamiltonian system under piecewise smooth polynomial perturbations.</p>

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Bifurcation of Limit Cycles from Quasi-Homogeneous Centers with Non-Smooth Perturbations

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Shengyu Chen,
  • Shiyou Sui

摘要

This paper estimates the number of limit cycles that bifurcate from periodic orbits of quasi-homogeneous centers under perturbations within the class of piecewise smooth polynomial systems of degree n. Using the first-order averaging method, we establish upper bounds for the number of limit cycles emerging from the period annuluses. As an application, the limit cycle bifurcation is studied for a quasi-homogeneous Hamiltonian system under piecewise smooth polynomial perturbations.