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Bifurcation of Limit Cycles from a Focus-Parabolic-Type Critical Point in Piecewise Smooth Cubic Systems

Author

Listed:
  • Fei Luo

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Yundong Li

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Yi Xiang

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

Abstract

In this paper, we investigate the maximum number of small-amplitude limit cycles bifurcated from a planar piecewise smooth focus-parabolic type cubic system that has one switching line given by the x -axis. By applying the generalized polar coordinates to the parabolic subsystem and computing the Lyapunov constants, we obtain 11 weak center conditions and 9 weak focus conditions at ( 0 , 0 ) . Under these conditions, we prove that a planar piecewise smooth cubic system with a focus-parabolic-type critical point can bifurcate at least nine limit cycles. So far, our result is a new lower bound of the cyclicity of the piecewise smooth focus-parabolic type cubic system.

Suggested Citation

  • Fei Luo & Yundong Li & Yi Xiang, 2024. "Bifurcation of Limit Cycles from a Focus-Parabolic-Type Critical Point in Piecewise Smooth Cubic Systems," Mathematics, MDPI, vol. 12(5), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:702-:d:1347594
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