Graphop mean-field limits and synchronization for the stochastic Kuramoto model
Gkogkas, Marios Antonios ; Jüttner, Benjamin ; Kuehn, Christian and Martens, Erik Andreas LU
(2022)
In Chaos
32(11).
- Abstract
Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition from incoherent to coherent oscillations under simplifying assumptions, including all-to-all coupling with uniform strength. Real world networks, however, often display heterogeneous connectivity and coupling weights that influence the critical threshold for this transition. We formulate a general mean-field theory (Vlasov-Focker Planck equation) for stochastic Kuramoto-type phase oscillator models, valid for coupling graphs/networks with heterogeneous connectivity and coupling strengths, using graphop... (More)
Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition from incoherent to coherent oscillations under simplifying assumptions, including all-to-all coupling with uniform strength. Real world networks, however, often display heterogeneous connectivity and coupling weights that influence the critical threshold for this transition. We formulate a general mean-field theory (Vlasov-Focker Planck equation) for stochastic Kuramoto-type phase oscillator models, valid for coupling graphs/networks with heterogeneous connectivity and coupling strengths, using graphop theory in the mean-field limit. Considering symmetric odd-valued coupling functions, we mathematically prove an exact formula for the critical threshold for the incoherence-coherence transition. We numerically test the predicted threshold using large finite-size representations of the network model. For a large class of graph models, we find that the numerical tests agree very well with the predicted threshold obtained from mean-field theory. However, the prediction is more difficult in practice for graph structures that are sufficiently sparse. Our findings open future research avenues toward a deeper understanding of mean-field theories for heterogeneous systems.
(Less)
- author
- Gkogkas, Marios Antonios
; Jüttner, Benjamin
; Kuehn, Christian
and Martens, Erik Andreas
LU
- organization
- publishing date
- 2022-11-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Chaos
- volume
- 32
- issue
- 11
- article number
- 113120
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:85143183261
- pmid:36456312
- ISSN
- 1054-1500
- DOI
- 10.1063/5.0094009
- language
- English
- LU publication?
- yes
- additional info
- Funding Information: M.A.G. and C.K. gratefully thank the TUM International Graduate School of Science and Engineering (IGSSE) for support via the project “Synchronization in Co-Evolutionary Network Dynamics (SEND).” B.J. and E.A.M. acknowledge the DTU International Graduate School for support via the EU-COFUND project “Synchronization in Co-Evolutionary Network Dynamics (SEND).” C.K. also acknowledges partial support by a Lichtenberg Professorship funded by the Volkswagen Stiftung. Publisher Copyright: © 2022 Author(s).
- id
- 093e3315-665f-4155-9048-3bd0fe230947
- date added to LUP
- 2022-12-13 18:25:46
- date last changed
- 2025-03-22 02:08:55
@article{093e3315-665f-4155-9048-3bd0fe230947,
abstract = {{<p>Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition from incoherent to coherent oscillations under simplifying assumptions, including all-to-all coupling with uniform strength. Real world networks, however, often display heterogeneous connectivity and coupling weights that influence the critical threshold for this transition. We formulate a general mean-field theory (Vlasov-Focker Planck equation) for stochastic Kuramoto-type phase oscillator models, valid for coupling graphs/networks with heterogeneous connectivity and coupling strengths, using graphop theory in the mean-field limit. Considering symmetric odd-valued coupling functions, we mathematically prove an exact formula for the critical threshold for the incoherence-coherence transition. We numerically test the predicted threshold using large finite-size representations of the network model. For a large class of graph models, we find that the numerical tests agree very well with the predicted threshold obtained from mean-field theory. However, the prediction is more difficult in practice for graph structures that are sufficiently sparse. Our findings open future research avenues toward a deeper understanding of mean-field theories for heterogeneous systems.</p>}},
author = {{Gkogkas, Marios Antonios and Jüttner, Benjamin and Kuehn, Christian and Martens, Erik Andreas}},
issn = {{1054-1500}},
language = {{eng}},
month = {{11}},
number = {{11}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Chaos}},
title = {{Graphop mean-field limits and synchronization for the stochastic Kuramoto model}},
url = {{http://dx.doi.org/10.1063/5.0094009}},
doi = {{10.1063/5.0094009}},
volume = {{32}},
year = {{2022}},
}