CENTERS AND LIMIT CYCLE BIFURCATIONS IN A FAMILY OF PIECEWISE SMOOTH SEPTIC <i>Z</i><sub>2</sub>-EQUIVARIANT SYSTEMS

Xue Zhang; Yusen Wu; Feng Li

doi:10.11948/20240193

2025 Volume 15 Issue 2

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Xue Zhang, Yusen Wu, Feng Li. CENTERS AND LIMIT CYCLE BIFURCATIONS IN A FAMILY OF PIECEWISE SMOOTH SEPTIC Z2-EQUIVARIANT SYSTEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 876-895. doi: 10.11948/20240193

Citation:

Xue Zhang, Yusen Wu, Feng Li. CENTERS AND LIMIT CYCLE BIFURCATIONS IN A FAMILY OF PIECEWISE SMOOTH SEPTIC Z₂-EQUIVARIANT SYSTEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 876-895. doi: 10.11948/20240193

CENTERS AND LIMIT CYCLE BIFURCATIONS IN A FAMILY OF PIECEWISE SMOOTH SEPTIC Z₂-EQUIVARIANT SYSTEMS

1.
School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276000, China
2.
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, China

Author Bio: Email: zhangxue031@163.com(X. Zhang); Email: wuyusen621@126.com(Y. Wu)
Corresponding author: Email: lifeng@lyu.edu.cn(F. Li)

Abstract

Abstract

In this paper, we investigate the center-focus problem and the number of limit cycles bifurcating from three foci for a family of piecewise smooth planar septic Z₂-equivariant systems, which include (±1, 0) and infinity as their singularities. We achieve a comprehensive classification of the conditions under which (±1, 0) act as centers. Moreover, we rigorously prove that, under small Z₂-equivariant perturbations, the perturbed system possesses at least 15 limit cycles, comprising 14 with small amplitude and 1 large amplitude with the scheme 1 ⊃ (7 ∪7).
- Center /
- limit cycle /
- bifurcation /
- Z₂-equivariant switching systems
MSC: 34C07, 37C23

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References

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