 Complex bifurcations and new types of structure uncovered in the Qi systemEnrui Zhang and Xianyi Li Mathematics and Computers in Simulation (MATCOM), 2026, vol. 244, issue C, 226-263 Abstract: In this paper, we revisit the Qi system and reveal its previously undiscovered complex dynamical characteristics. We first rigorously characterize the precise distribution of its equilibria in its total parameter space, then completely analyze the stability of all of its equilibria. Next, what is more important, we investigate its bifurcation problems concerning both the quantity of equilibria and stability boundaries, further analyzing codimension-two bifurcations between subcritical and supercritical pitchfork bifurcations, as well as codimension-three Hopf bifurcations. Finally, through numerical encoding of system trajectory, we generate biparametric sweep that unveils several remarkable phenomena deserving deeper exploration, where, most significantly, we first in the Qi system discover intriguing and new structures: self-similar UII-shaped structure and shrimp-shaped structure. Keywords: Qi system; Pitchfork bifurcation; Codimension-three Hopf bifurcation; Chaos; Homoclinic orbit; Biparametric sweep; Self-similar UII-shaped structure; Shrimp-shaped structure (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:matcom:v:244:y:2026:i:c:p:226-263 DOI: 10.1016/j.matcom.2025.12.013 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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