Centers and Limit Cycle Bifurcations in a Family of Piecewise Smooth Septic Z2-equivariant Systems
Year: 2025
Type: article
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).
DOI: 10.11948/20240193
Authors: Xue Zhang, Yusen Wu, Feng Li
Institutions: Linyi University, Henan University of Science and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411533639