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Complex bifurcations and new types of structure uncovered in the Qi system

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  • Zhang, Enrui
  • Li, Xianyi

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.

Suggested Citation

  • Zhang, Enrui & Li, Xianyi, 2026. "Complex bifurcations and new types of structure uncovered in the Qi system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 244(C), pages 226-263.
    • Handle: RePEc:eee:matcom:v:244:y:2026:i:c:p:226-263
    DOI: 10.1016/j.matcom.2025.12.013
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    1. Wu, Wen-Juan & Chen, Zeng-Qiang & Yuan, Zhu-Zhi, 2009. "A computer-assisted proof for the existence of horseshoe in a novel chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2756-2761.
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