Modeling, analysis, and control of networked dynamical systems
In his PhD thesis Shaoxuan Cui develops new modeling, analysis, and control tools for networked dynamical systems by moving beyond traditional graph models (pairwise interactions) to higher-order interactions captured by hypergraphs and tensors.
Cui's thesis is organized in two parts: (i) extensions of classical graph-based frameworks to time-varying and interconnected network dynamics, and (ii) a unified tensor/hypergraph perspective for nonlinear diffusion and spreading, collective coordination and Laplacian-type dynamics, and evolutionary population dynamics.
A central message in the thesis is that higher-order representations are not just a small refinement of graphs: by explicitly representing group-level synergies and antagonisms, they can produce qualitatively new phenomena such as multistability, richer bifurcation patterns, and altered stability/attraction regions that do not arise in pairwise models.
Cui also advances tensor-spectral tools, distinguishing eigenvalue notions suited to continuous- vs. discrete-time systems (e.g., H- vs. Z-eigenvalues), and uses them to extend Perron–Frobenius and Laplacian ideas from graphs to hypergraphs.
The work highlights both the opportunities and the open challenges ahead, especially scalable computation and data-driven reconstruction of higher-order structures.