Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 33 min ago
PreprintarXiv licencearXiv

Cyclicity of centers on center manifolds in a 3D chaotic system with a four-wing attractor

  • Vitor Gusson
  • Claudio Pessoa
Open at sourcePDFDOICite

Abstract

In this work, we investigate the conditions that guarantee the existence of centers on the center manifold, arising from Hopf points, in the new three-dimensional quadratic chaotic system introduced by B. Khaled et al. in 2024 in the Int. J. Data Netw. Sci. For some of the Hopf points of the system, we solve the center-focus problem on the center manifold, analyzing both its isochronicity and cyclicity. Our results significantly improve the previously known lower bound on the number of limit cycles bifurcating from Hopf points in this system, as established by B. M. Mohammed in 2025 in the Int. J. Bifurc. Chaos Appl. Sci. Eng.

Related

  1. Cyclicity of lips and center-focus problem at infinity
    Hebai Chen, Dehong Dai, Vadim Kaloshin +1
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  2. Linear transformations of tropical matrices preserving individual values of the cyclicity index
    Alexander Guterman, Alexander Vlasov, Svetlana Zhilina
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Cyclicity of Drinfeld modules modulo primes in arithmetic progressions
    Prassanna Nand Jha, Arnab Saha, Akshaa Vatwani
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. On The Cyclicity of Algebraic Lattices
    Maria Fernanda Zordan Bonini, Robson Ricardo de Araujo, Antonio Aparecido de Andrade +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. On the Cyclicity Conjecture
    Alexander Dobrick
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{gusson2026cyclicity,
  title = {{Cyclicity of centers on center manifolds in a 3D chaotic system with a four-wing attractor}},
  author = {Vitor Gusson and Claudio Pessoa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.08929},
  eprint = {2605.08929},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.08929},
}
RIS
TY  - UNPB
TI  - Cyclicity of centers on center manifolds in a 3D chaotic system with a four-wing attractor
AU  - Vitor Gusson
AU  - Claudio Pessoa
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2605.08929
UR  - https://arxiv.org/abs/2605.08929
AB  - In this work, we investigate the conditions that guarantee the existence of centers on the center manifold, arising from Hopf points, in the new three-dimensional quadratic chaotic system introduced by B. Khaled et al. in 2024 in the Int. J. Data Netw. Sci. For some of the Hopf points of the system, we solve the center-focus problem on the center manifold, analyzing both its isochronicity and cyclicity. Our results significantly improve the previously known lower bound on the number of limit cycles bifurcating from Hopf points in this system, as established by B. M. Mohammed in 2025 in the Int. J. Bifurc. Chaos Appl. Sci. Eng.
ER  -