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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
Organizers
Speaker
Prof. Xianyi Li
Time
Friday, June 13, 2025 5:01 PM - 6:00 PM
Venue
A3-1-301
Online
Zoom 468 248 1222
(BIMSA)
Abstract
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.