A frequency domain analysis of slow coherency in networked systems
(2025) In Automatica 174.- Abstract
Network coherence generally refers to the emergence of simple aggregated dynamical behaviors, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property of the system's input–output response. More precisely, for a networked system with linear dynamics and coupling, we show that, as the network's frequency-dependent algebraic connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior. Interestingly, the non-zero eigenvalue of such a rank-one matrix is given by the... (More)
Network coherence generally refers to the emergence of simple aggregated dynamical behaviors, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property of the system's input–output response. More precisely, for a networked system with linear dynamics and coupling, we show that, as the network's frequency-dependent algebraic connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior. 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 coherent dynamics. Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology. We further show that many networked systems can exhibit similar coherent behavior by establishing a concentration result in a setting with randomly chosen individual nodal dynamics.
(Less)
- author
- Min, Hancheng ; Pates, Richard LU and Mallada, Enrique
- organization
- publishing date
- 2025-04
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Large-scale networks, Linear/nonlinear model, Low-rank approximation, Multi-agent systems, Slow coherency
- in
- Automatica
- volume
- 174
- article number
- 112184
- publisher
- Elsevier
- external identifiers
-
- scopus:85216794057
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2025.112184
- language
- English
- LU publication?
- yes
- id
- 498de66e-520f-4ab0-8714-8cb667d2bbc4
- date added to LUP
- 2025-03-21 09:41:33
- date last changed
- 2025-04-04 14:20:39
@article{498de66e-520f-4ab0-8714-8cb667d2bbc4,
abstract = {{<p>Network coherence generally refers to the emergence of simple aggregated dynamical behaviors, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property of the system's input–output response. More precisely, for a networked system with linear dynamics and coupling, we show that, as the network's frequency-dependent algebraic connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior. 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 coherent dynamics. Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology. We further show that many networked systems can exhibit similar coherent behavior by establishing a concentration result in a setting with randomly chosen individual nodal dynamics.</p>}},
author = {{Min, Hancheng and Pates, Richard and Mallada, Enrique}},
issn = {{0005-1098}},
keywords = {{Large-scale networks; Linear/nonlinear model; Low-rank approximation; Multi-agent systems; Slow coherency}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Automatica}},
title = {{A frequency domain analysis of slow coherency in networked systems}},
url = {{http://dx.doi.org/10.1016/j.automatica.2025.112184}},
doi = {{10.1016/j.automatica.2025.112184}},
volume = {{174}},
year = {{2025}},
}