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Seminar on Statistics and Data Analysis
Complex bifurcations and new types of structure discovered in the Qi system
Complex bifurcations and new types of structure discovered in the Qi system
组织者
演讲者
Prof. Xianyi Li
时间
2025年06月13日 17:01 至 18:00
地点
A3-1-301
线上
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(BIMSA)
摘要
In this talk, we revisit the Qi system and reveal its previously undiscovered complex dynamical properties. 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's 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 discover in the Qi system intriguing and new types of structure: self-similar UII-shaped structure and shrimp-shaped structure.