Identifying Network Structure of Nonlinear Dynamical Systems: Contraction and Kuramoto Oscillators
This addresses the fundamental challenge of network identifiability in complex systems like biological or social networks, but it appears incremental as it builds on existing contraction theory.
The paper tackles the problem of identifying network structures in nonlinear dynamical systems when only partial measurements are available, showing that semicontraction in the observable space makes different network topologies indistinguishable. It applies this framework to Kuramoto oscillator networks, demonstrating scenarios where both connected and disconnected structures become indistinguishable.
In this work, we study the identifiability of network structures (i.e., topologies) for networked nonlinear systems when partial measurements of the nodal dynamics are taken. We explore scenarios where different candidate structures can yield similar measurements, thus limiting identifiability. To do so, we apply the contraction theory framework to facilitate comparisons between different networks. We show that semicontraction in the observable space is a sufficient condition for two systems to become indistinguishable from one another based on partial measurements. We apply this framework to study networks of Kuramoto oscillators, and discuss scenarios in which different network structures (both connected and disconnected) become indistinguishable.