| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0193 |
| Centers and limit cycle bifurcations in a family of septic Z2-equivariant systems with four switching lines |
| Xue Zhang,Feng Li |
| Keywords:Center Limit cycle Bifurcation Z2-Equivariant switching systems |
| 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 $Z_2$-equivariant systems, which include
$(\pm1,0)$ and infinity as their singularities. We achieve
a comprehensive classification of the conditions under which $(\pm1,0)$ act as
centers. Moreover, we rigorously prove that, under small $Z_2$-equivariant
perturbations, the perturbed system possesses at least
15 limit cycles, comprising 14 with small amplitude and 1 large amplitude with the scheme, following the scheme $1\supset(7\,\cup7)$. |
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