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Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding co...

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Autores principales: Budzinski, Roberto C., Nguyen, Tung T., Đoàn, Jacqueline, Mináč, Ján, Sejnowski, Terrence J., Muller, Lyle E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: AIP Publishing LLC 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947818/
https://www.ncbi.nlm.nih.gov/pubmed/35364855
http://dx.doi.org/10.1063/5.0078791
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author Budzinski, Roberto C.
Nguyen, Tung T.
Đoàn, Jacqueline
Mináč, Ján
Sejnowski, Terrence J.
Muller, Lyle E.
author_facet Budzinski, Roberto C.
Nguyen, Tung T.
Đoàn, Jacqueline
Mináč, Ján
Sejnowski, Terrence J.
Muller, Lyle E.
author_sort Budzinski, Roberto C.
collection PubMed
description One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.
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spelling pubmed-89478182022-04-04 Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks Budzinski, Roberto C. Nguyen, Tung T. Đoàn, Jacqueline Mináč, Ján Sejnowski, Terrence J. Muller, Lyle E. Chaos Fast Track One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems. AIP Publishing LLC 2022-03 2022-03-23 /pmc/articles/PMC8947818/ /pubmed/35364855 http://dx.doi.org/10.1063/5.0078791 Text en © 2022 Author(s). https://creativecommons.org/licenses/by/4.0/All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Fast Track
Budzinski, Roberto C.
Nguyen, Tung T.
Đoàn, Jacqueline
Mináč, Ján
Sejnowski, Terrence J.
Muller, Lyle E.
Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
title Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
title_full Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
title_fullStr Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
title_full_unstemmed Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
title_short Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
title_sort geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
topic Fast Track
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947818/
https://www.ncbi.nlm.nih.gov/pubmed/35364855
http://dx.doi.org/10.1063/5.0078791
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