Modeling, Analysis, and Control of Networked Dynamical Systems

This PhD thesis 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. It 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 is that higher-order representations are not 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. The thesis 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.