Johns Hopkins University
Coherence and Concentration in Tightly Connected Networks
2:30 pm, Room St Clair 3B
Achieving coordinated behavior— engineered or emergent—on networked systems has attracted widespread interest in several fields. This interest has led to remarkable advances in developing a theoretical understanding of the conditions under which agents within a network can reach an agreement (consensus) or develop coordinated behavior, such as synchronization. However, much less understood is the phenomenon of network coherence. Network coherence generally refers to nodes’ ability in a network to have a similar dynamic response despite heterogeneity in their behavior. In this talk, we present a general framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property. More precisely, for a networked system with linear dynamics and coupling, we show that the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior as the network connectivity grows. Interestingly, the non-zero eigenvalue of such a rank-one matrix is given by the harmonic mean of individual nodal dynamics, and we refer to it as the coherent dynamics. Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology. We further illustrate how this framework can be leveraged for obtaining accurate reduced-order models of coherent generators and tuning grid forming inverters to shape the (coherent) frequency response in power grids.