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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...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
AIP Publishing LLC
2022
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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. |
format | Online Article Text |
id | pubmed-8947818 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | AIP Publishing LLC |
record_format | MEDLINE/PubMed |
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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