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

Xiaowei Li and Xingbo Liu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 583-603

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.

Keywords: Limit cycles; Linear isochronous center; Cubic isochronous centers; Piecewise smooth differential system; Bifurcation (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:583-603

DOI: 10.1016/j.matcom.2026.04.045

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