 Weak centers and local criticality on planar Z2-symmetric cubic differential systemsYuanyuan Liu, Dongping He and Wentao Huang Chaos, Solitons & Fractals, 2023, vol. 177, issue C Abstract: There exist the necessary and sufficient conditions for planar Z2-symmetric cubic differential systems with a bi-center and an isochronous bi-center in the existing literature. Based on these bi-center conditions, we give a complete discussion on the order of weak centers and the local criticality for planar Z2-symmetric cubic systems at the origin and the symmetric equilibria (±1,0) separately. More precisely, we first give the parametric conditions for the origin and the equilibria (±1,0) being weak centers of exact order separately. Then we prove that the local criticality from the weak centers of finite order at the origin is at most 4, and at each of symmetric equilibria (±1,0) is at most 3. Finally, we also obtain that the local criticality from the isochronous center at the origin is at most 3, and at each of equilibria (±1,0) is at least 2. More importantly, these numbers are reachable. Keywords: Z2-symmetric cubic systems; Complex period constants; Local criticality; Weak center; Isochronous center (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011591 DOI: 10.1016/j.chaos.2023.114257 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.