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<p>In this paper, we investigate the classical problem related to bifurcation of small-amplitude limit cycles in a class of piecewise smooth cubic Rayleigh-Liénard systems. By using the developed Poincaré-Lyapunov method, we achieve the classifications of the center at the origin of such piecewise smooth polynomial system. We further provide the necessary and sufficient conditions of the global center. Furthermore, we establish that lower bound on the maximum number of limit cycles bifurcating from the origin is 5.</p>

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Bifurcation of Limit Cycles in a Class of Piecewise Smooth Cubic Rayleigh-Liénard Systems

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Fang Wu,
  • Ting Chen,
  • Xin Li

摘要

In this paper, we investigate the classical problem related to bifurcation of small-amplitude limit cycles in a class of piecewise smooth cubic Rayleigh-Liénard systems. By using the developed Poincaré-Lyapunov method, we achieve the classifications of the center at the origin of such piecewise smooth polynomial system. We further provide the necessary and sufficient conditions of the global center. Furthermore, we establish that lower bound on the maximum number of limit cycles bifurcating from the origin is 5.