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Limit cycle bifurcation in piecewise differential systems formed by linear and cubic isochronous centers

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  • Li, Xiaowei
  • Liu, Xingbo

Abstract

In this paper, we study the piecewise smooth systems separated by a straight line and formed by combinations of linear isochronous center and cubic isochronous centers. Compared with the work of Buzzi et al., (2022), where the maximum number of crossing limit cycles of some classes for such systems was studied, we consider the classes that the systems have a family of periodic orbits surrounding the origin. By means of the displacement function and expansion technique, we obtain a lower bound for the number of limit cycles bifurcated from these periodic orbits under piecewise quadratic perturbations, without dealing with the relatively difficult integrals inherent in the usual averaging approach.

Suggested Citation

  • Li, Xiaowei & Liu, Xingbo, 2026. "Limit cycle bifurcation in piecewise differential systems formed by linear and cubic isochronous centers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 583-603.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:583-603
    DOI: 10.1016/j.matcom.2026.04.045
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    References listed on IDEAS

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    1. Ito, Takatoshi, 1979. "A Filippov solution of a system of differential equations with discontinuous right-hand sides," Economics Letters, Elsevier, vol. 4(4), pages 349-354.
    2. Llibre, Jaume & Valls, Claudia, 2022. "Crossing limit cycles for discontinuous piecewise differential systems formed by linear Hamiltonian saddles or linear centers separated by a conic," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. He, Dongping & Llibre, Jaume, 2025. "Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I)," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 743-757.
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