Kuramoto model (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kuramoto model" in English language version.

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28doi.org

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16harvard.edu

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3handle.net

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1stevenstrogatz.com

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aip.org

pubs.aip.org

Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.

arxiv.org

Bick, Christian; Goodfellow, Marc; Laing, Carlo R.; Martens, Erik A. (2020). "Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review". Journal of Mathematical Neuroscience. 10 (1): 9. arXiv:1902.05307. doi:10.1186/s13408-020-00086-9. PMC 7253574. PMID 32462281.
Forrester, D.M. (2015). "Arrays of coupled chemical oscillators". Scientific Reports. 5: 16994. arXiv:1606.01556. Bibcode:2015NatSR...516994F. doi:10.1038/srep16994. PMC 4652215. PMID 26582365.
Witthaut, Dirk; Timme, Marc (2014). "Kuramoto Dynamics in Hamiltonian Systems". Phys. Rev. E. 90 (3): 032917. arXiv:1305.1742. Bibcode:2014PhRvE..90c2917W. doi:10.1103/PhysRevE.90.032917. PMID 25314514. S2CID 7510614.
Rodrigues, F. A.; Peron, T.K.; Jie, P.; Kurths, J. (2016). "The Kuramoto model in complex networks". Physics Reports. 610 (1): 1–98. arXiv:1511.07139. Bibcode:2016PhR...610....1R. doi:10.1016/j.physrep.2015.10.008. S2CID 119290926.
Abrams, D.M.; Strogatz, S.H. (2004). "Chimera states for coupled oscillators". Physical Review Letters. 93 (17): 174102. arXiv:nlin/0407045. Bibcode:2004PhRvL..93q4102A. doi:10.1103/physrevlett.93.174102. PMID 15525081. S2CID 8615112.
Eom, Y.-H.; Boccaletti, S.; Caldarelli, G (2016). "Concurrent enhancement of percolation and synchronization in adaptive networks". Scientific Reports. 7: 015103. arXiv:1511.05468. Bibcode:2016NatSR...627111E. doi:10.1038/srep27111. PMC 4890019. PMID 27251577.
Canale, Eduardo A. (2022). "From weighted to unweighted graphs in Synchronizing Graph Theory". arXiv:2209.06362 [math.CO].
Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.
Ling, Shuyang; Xu, Ruitu; Bandeira, Afonso S. (January 2019). "On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization". SIAM Journal on Optimization. 29 (3): 1879–1907. arXiv:1809.11083. doi:10.1137/18M1217644. ISSN 1052-6234. S2CID 53067184.
Abdalla, Pedro; Bandeira, Afonso S.; Kassabov, Martin; Souza, Victor; Strogatz, Steven H.; Townsend, Alex (2022). "Expander graphs are globally synchronising". arXiv:2210.12788 [math.CO].
Menara, T.; Baggio, G.; Bassett, D.; Pasqualetti, F. (2020). "Stability Conditions for Cluster Synchronizations in Networks of Heterogeneous Kuramoto Oscillators". IEEE Transactions on Control of Network Systems. 7 (1): 302–314. arXiv:1806.06083. doi:10.1109/TCNS.2019.2903914. S2CID 73729229.
Clusella, Pau; Politi, Antonio; Rosenblum, Michael (2016). "A minimal model of self-consistent partial synchrony". New Journal of Physics. 18 (9): 093037. arXiv:1607.07178. Bibcode:2016NJPh...18i3037C. doi:10.1088/1367-2630/18/9/093037. ISSN 1367-2630. S2CID 126227664.
Bick, C.; Timme, M.; Paulikat, D.; Rathlev, D.; Ashwin, P. (2011). "Chaos in Symmetric Phase Oscillator Networks". Physical Review Letters. 107 (24): 244101. arXiv:1105.2230. Bibcode:2011PhRvL.107x4101B. doi:10.1103/PhysRevLett.107.244101. PMID 22243002. S2CID 16144737.

doi.org

Strogatz, Steven H. (2000). "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators". Physica D. 143 (1–4): 1–20. Bibcode:2000PhyD..143....1S. doi:10.1016/S0167-2789(00)00094-4. S2CID 16668746. Retrieved 2024-01-04.
Acebrón, Juan A.; Bonilla, L. L.; Vicente, Pérez; Conrad, J.; Ritort, Félix; Spigler, Renato (2005). "The Kuramoto model: A simple paradigm for synchronization phenomena" (PDF). Reviews of Modern Physics. 77 (1): 137–185. Bibcode:2005RvMP...77..137A. doi:10.1103/RevModPhys.77.137. hdl:2445/12768.
Bick, Christian; Goodfellow, Marc; Laing, Carlo R.; Martens, Erik A. (2020). "Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review". Journal of Mathematical Neuroscience. 10 (1): 9. arXiv:1902.05307. doi:10.1186/s13408-020-00086-9. PMC 7253574. PMID 32462281.
Cumin, D.; Unsworth, C. P. (2007). "Generalising the Kuromoto model for the study of neuronal synchronisation in the brain". Physica D. 226 (2): 181–196. Bibcode:2007PhyD..226..181C. doi:10.1016/j.physd.2006.12.004. hdl:2292/2666.
Breakspear M, Heitmann S, Daffertshofer A (2010). "Generative models of cortical oscillations: Neurobiological implications of the Kuramoto model". Front Hum Neurosci. 4 (190): 190. doi:10.3389/fnhum.2010.00190. PMC 2995481. PMID 21151358.
Cabral J, Luckhoo H, Woolrich M, Joensson M, Mohseni H, Baker A, Kringelbach ML, Deco G (2014). "Exploring mechanisms of spontaneous functional connectivity in MEG: How delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations". NeuroImage. 90: 423–435. doi:10.1016/j.neuroimage.2013.11.047. hdl:10230/23081. PMID 24321555.
Sivashinsky, G.I. (1977). "Diffusional-thermal theory of cellular flames". Combust. Sci. Technol. 15 (3–4): 137–146. doi:10.1080/00102207708946779.
Forrester, D.M. (2015). "Arrays of coupled chemical oscillators". Scientific Reports. 5: 16994. arXiv:1606.01556. Bibcode:2015NatSR...516994F. doi:10.1038/srep16994. PMC 4652215. PMID 26582365.
Strogatz, Steven H. (1994). "Norbert Wiener's Brain Waves". In Levin, Simon A. (ed.). Frontiers in Mathematical Biology. Lecture Notes in Biomathematics. Vol. 100. Berlin, Heidelberg: Springer. pp. 122–138. doi:10.1007/978-3-642-50124-1_7. ISBN 978-3-642-50124-1.
Maistrenko, Yuri L.; Popovych, Oleksandr V.; Tass, Peter A. (November 2005). "Chaotic Attractor in the Kuramoto Model". International Journal of Bifurcation and Chaos. 15 (11): 3457–3466. Bibcode:2005IJBC...15.3457M. doi:10.1142/S0218127405014155. ISSN 0218-1274.
Witthaut, Dirk; Timme, Marc (2014). "Kuramoto Dynamics in Hamiltonian Systems". Phys. Rev. E. 90 (3): 032917. arXiv:1305.1742. Bibcode:2014PhRvE..90c2917W. doi:10.1103/PhysRevE.90.032917. PMID 25314514. S2CID 7510614.
Rodrigues, F. A.; Peron, T.K.; Jie, P.; Kurths, J. (2016). "The Kuramoto model in complex networks". Physics Reports. 610 (1): 1–98. arXiv:1511.07139. Bibcode:2016PhR...610....1R. doi:10.1016/j.physrep.2015.10.008. S2CID 119290926.
Abrams, D.M.; Strogatz, S.H. (2004). "Chimera states for coupled oscillators". Physical Review Letters. 93 (17): 174102. arXiv:nlin/0407045. Bibcode:2004PhRvL..93q4102A. doi:10.1103/physrevlett.93.174102. PMID 15525081. S2CID 8615112.
Kazanci, F.; Ermentrout, B. (2006). "Pattern formation in an array of oscillators with electrical and chemical coupling". SIAM J Appl Math. 67 (2): 512–529. CiteSeerX 10.1.1.140.1020. doi:10.1137/060661041.
Heitmann, S.; Gong, P.; Breakspear, M (2012). "A computational role for bistability and traveling waves in motor cortex". Front Comput Neurosci. 6 (67): 67. doi:10.3389/fncom.2012.00067. PMC 3438483. PMID 22973223.
Heitmann, S.; Ermentrout, B. (2015). "Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity". Biological Cybernetics. 109 (3): 1–15. doi:10.1007/s00422-015-0646-6. PMID 25677527. S2CID 18561153.
Wiley, D.; Strogatz, S.; Girvan, M (2006). "The size of the sync basin". Chaos. 16 (1): 015103. Bibcode:2006Chaos..16a5103W. doi:10.1063/1.2165594. PMID 16599769. S2CID 21173189.
Eom, Y.-H.; Boccaletti, S.; Caldarelli, G (2016). "Concurrent enhancement of percolation and synchronization in adaptive networks". Scientific Reports. 7: 015103. arXiv:1511.05468. Bibcode:2016NatSR...627111E. doi:10.1038/srep27111. PMC 4890019. PMID 27251577.
Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.
Ling, Shuyang; Xu, Ruitu; Bandeira, Afonso S. (January 2019). "On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization". SIAM Journal on Optimization. 29 (3): 1879–1907. arXiv:1809.11083. doi:10.1137/18M1217644. ISSN 1052-6234. S2CID 53067184.
Pantaleone, James (October 2002). "Synchronization of metronomes" (PDF). American Journal of Physics. 70 (10): 992–1000. Bibcode:2002AmJPh..70..992P. doi:10.1119/1.1501118.
Dorfler, F.; Bullo, F. (2014). "Synchronization in complex networks of phase oscillators: A survey". Automatica. 50 (6): 1539–1564. doi:10.1016/j.automatica.2014.04.012.
Menara, T.; Baggio, G.; Bassett, D.; Pasqualetti, F. (2020). "Stability Conditions for Cluster Synchronizations in Networks of Heterogeneous Kuramoto Oscillators". IEEE Transactions on Control of Network Systems. 7 (1): 302–314. arXiv:1806.06083. doi:10.1109/TCNS.2019.2903914. S2CID 73729229.
Cabral, J.; Hugues, E.; Sporns, O.; Deco, G. (2011). "Role of local network oscillations in resting-state functional connectivity". NeuroImage. 57 (1): 130–139. doi:10.1016/j.neuroimage.2011.04.010. PMID 21511044. S2CID 13959959.
Hansel, D.; Mato, G.; Meunier, C (1993). "Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons". Europhysics Letters. 23 (5): 367–372. Bibcode:1993EL.....23..367H. doi:10.1209/0295-5075/23/5/011. S2CID 250884499.
Clusella, Pau; Politi, Antonio; Rosenblum, Michael (2016). "A minimal model of self-consistent partial synchrony". New Journal of Physics. 18 (9): 093037. arXiv:1607.07178. Bibcode:2016NJPh...18i3037C. doi:10.1088/1367-2630/18/9/093037. ISSN 1367-2630. S2CID 126227664.
Hansel, D.; Mato, G.; Meunier, C (1993). "Clustering and slow switching in globally coupled phase oscillators" (PDF). Physical Review E. 48 (5): 3470–3477. Bibcode:1993PhRvE..48.3470H. doi:10.1103/physreve.48.3470. PMID 9961005.
Bick, C.; Timme, M.; Paulikat, D.; Rathlev, D.; Ashwin, P. (2011). "Chaos in Symmetric Phase Oscillator Networks". Physical Review Letters. 107 (24): 244101. arXiv:1105.2230. Bibcode:2011PhRvL.107x4101B. doi:10.1103/PhysRevLett.107.244101. PMID 22243002. S2CID 16144737.

hal.science

Hansel, D.; Mato, G.; Meunier, C (1993). "Clustering and slow switching in globally coupled phase oscillators" (PDF). Physical Review E. 48 (5): 3470–3477. Bibcode:1993PhRvE..48.3470H. doi:10.1103/physreve.48.3470. PMID 9961005.

handle.net

hdl.handle.net

Acebrón, Juan A.; Bonilla, L. L.; Vicente, Pérez; Conrad, J.; Ritort, Félix; Spigler, Renato (2005). "The Kuramoto model: A simple paradigm for synchronization phenomena" (PDF). Reviews of Modern Physics. 77 (1): 137–185. Bibcode:2005RvMP...77..137A. doi:10.1103/RevModPhys.77.137. hdl:2445/12768.
Cumin, D.; Unsworth, C. P. (2007). "Generalising the Kuromoto model for the study of neuronal synchronisation in the brain". Physica D. 226 (2): 181–196. Bibcode:2007PhyD..226..181C. doi:10.1016/j.physd.2006.12.004. hdl:2292/2666.
Cabral J, Luckhoo H, Woolrich M, Joensson M, Mohseni H, Baker A, Kringelbach ML, Deco G (2014). "Exploring mechanisms of spontaneous functional connectivity in MEG: How delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations". NeuroImage. 90: 423–435. doi:10.1016/j.neuroimage.2013.11.047. hdl:10230/23081. PMID 24321555.

harvard.edu

ui.adsabs.harvard.edu

Strogatz, Steven H. (2000). "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators". Physica D. 143 (1–4): 1–20. Bibcode:2000PhyD..143....1S. doi:10.1016/S0167-2789(00)00094-4. S2CID 16668746. Retrieved 2024-01-04.
Acebrón, Juan A.; Bonilla, L. L.; Vicente, Pérez; Conrad, J.; Ritort, Félix; Spigler, Renato (2005). "The Kuramoto model: A simple paradigm for synchronization phenomena" (PDF). Reviews of Modern Physics. 77 (1): 137–185. Bibcode:2005RvMP...77..137A. doi:10.1103/RevModPhys.77.137. hdl:2445/12768.
Cumin, D.; Unsworth, C. P. (2007). "Generalising the Kuromoto model for the study of neuronal synchronisation in the brain". Physica D. 226 (2): 181–196. Bibcode:2007PhyD..226..181C. doi:10.1016/j.physd.2006.12.004. hdl:2292/2666.
Forrester, D.M. (2015). "Arrays of coupled chemical oscillators". Scientific Reports. 5: 16994. arXiv:1606.01556. Bibcode:2015NatSR...516994F. doi:10.1038/srep16994. PMC 4652215. PMID 26582365.
Maistrenko, Yuri L.; Popovych, Oleksandr V.; Tass, Peter A. (November 2005). "Chaotic Attractor in the Kuramoto Model". International Journal of Bifurcation and Chaos. 15 (11): 3457–3466. Bibcode:2005IJBC...15.3457M. doi:10.1142/S0218127405014155. ISSN 0218-1274.
Witthaut, Dirk; Timme, Marc (2014). "Kuramoto Dynamics in Hamiltonian Systems". Phys. Rev. E. 90 (3): 032917. arXiv:1305.1742. Bibcode:2014PhRvE..90c2917W. doi:10.1103/PhysRevE.90.032917. PMID 25314514. S2CID 7510614.
Rodrigues, F. A.; Peron, T.K.; Jie, P.; Kurths, J. (2016). "The Kuramoto model in complex networks". Physics Reports. 610 (1): 1–98. arXiv:1511.07139. Bibcode:2016PhR...610....1R. doi:10.1016/j.physrep.2015.10.008. S2CID 119290926.
Abrams, D.M.; Strogatz, S.H. (2004). "Chimera states for coupled oscillators". Physical Review Letters. 93 (17): 174102. arXiv:nlin/0407045. Bibcode:2004PhRvL..93q4102A. doi:10.1103/physrevlett.93.174102. PMID 15525081. S2CID 8615112.
Wiley, D.; Strogatz, S.; Girvan, M (2006). "The size of the sync basin". Chaos. 16 (1): 015103. Bibcode:2006Chaos..16a5103W. doi:10.1063/1.2165594. PMID 16599769. S2CID 21173189.
Eom, Y.-H.; Boccaletti, S.; Caldarelli, G (2016). "Concurrent enhancement of percolation and synchronization in adaptive networks". Scientific Reports. 7: 015103. arXiv:1511.05468. Bibcode:2016NatSR...627111E. doi:10.1038/srep27111. PMC 4890019. PMID 27251577.
Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.
Pantaleone, James (October 2002). "Synchronization of metronomes" (PDF). American Journal of Physics. 70 (10): 992–1000. Bibcode:2002AmJPh..70..992P. doi:10.1119/1.1501118.
Hansel, D.; Mato, G.; Meunier, C (1993). "Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons". Europhysics Letters. 23 (5): 367–372. Bibcode:1993EL.....23..367H. doi:10.1209/0295-5075/23/5/011. S2CID 250884499.
Clusella, Pau; Politi, Antonio; Rosenblum, Michael (2016). "A minimal model of self-consistent partial synchrony". New Journal of Physics. 18 (9): 093037. arXiv:1607.07178. Bibcode:2016NJPh...18i3037C. doi:10.1088/1367-2630/18/9/093037. ISSN 1367-2630. S2CID 126227664.
Hansel, D.; Mato, G.; Meunier, C (1993). "Clustering and slow switching in globally coupled phase oscillators" (PDF). Physical Review E. 48 (5): 3470–3477. Bibcode:1993PhRvE..48.3470H. doi:10.1103/physreve.48.3470. PMID 9961005.
Bick, C.; Timme, M.; Paulikat, D.; Rathlev, D.; Ashwin, P. (2011). "Chaos in Symmetric Phase Oscillator Networks". Physical Review Letters. 107 (24): 244101. arXiv:1105.2230. Bibcode:2011PhRvL.107x4101B. doi:10.1103/PhysRevLett.107.244101. PMID 22243002. S2CID 16144737.

nih.gov

pubmed.ncbi.nlm.nih.gov

Bick, Christian; Goodfellow, Marc; Laing, Carlo R.; Martens, Erik A. (2020). "Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review". Journal of Mathematical Neuroscience. 10 (1): 9. arXiv:1902.05307. doi:10.1186/s13408-020-00086-9. PMC 7253574. PMID 32462281.
Breakspear M, Heitmann S, Daffertshofer A (2010). "Generative models of cortical oscillations: Neurobiological implications of the Kuramoto model". Front Hum Neurosci. 4 (190): 190. doi:10.3389/fnhum.2010.00190. PMC 2995481. PMID 21151358.
Cabral J, Luckhoo H, Woolrich M, Joensson M, Mohseni H, Baker A, Kringelbach ML, Deco G (2014). "Exploring mechanisms of spontaneous functional connectivity in MEG: How delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations". NeuroImage. 90: 423–435. doi:10.1016/j.neuroimage.2013.11.047. hdl:10230/23081. PMID 24321555.
Forrester, D.M. (2015). "Arrays of coupled chemical oscillators". Scientific Reports. 5: 16994. arXiv:1606.01556. Bibcode:2015NatSR...516994F. doi:10.1038/srep16994. PMC 4652215. PMID 26582365.
Witthaut, Dirk; Timme, Marc (2014). "Kuramoto Dynamics in Hamiltonian Systems". Phys. Rev. E. 90 (3): 032917. arXiv:1305.1742. Bibcode:2014PhRvE..90c2917W. doi:10.1103/PhysRevE.90.032917. PMID 25314514. S2CID 7510614.
Abrams, D.M.; Strogatz, S.H. (2004). "Chimera states for coupled oscillators". Physical Review Letters. 93 (17): 174102. arXiv:nlin/0407045. Bibcode:2004PhRvL..93q4102A. doi:10.1103/physrevlett.93.174102. PMID 15525081. S2CID 8615112.
Heitmann, S.; Gong, P.; Breakspear, M (2012). "A computational role for bistability and traveling waves in motor cortex". Front Comput Neurosci. 6 (67): 67. doi:10.3389/fncom.2012.00067. PMC 3438483. PMID 22973223.
Heitmann, S.; Ermentrout, B. (2015). "Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity". Biological Cybernetics. 109 (3): 1–15. doi:10.1007/s00422-015-0646-6. PMID 25677527. S2CID 18561153.
Wiley, D.; Strogatz, S.; Girvan, M (2006). "The size of the sync basin". Chaos. 16 (1): 015103. Bibcode:2006Chaos..16a5103W. doi:10.1063/1.2165594. PMID 16599769. S2CID 21173189.
Eom, Y.-H.; Boccaletti, S.; Caldarelli, G (2016). "Concurrent enhancement of percolation and synchronization in adaptive networks". Scientific Reports. 7: 015103. arXiv:1511.05468. Bibcode:2016NatSR...627111E. doi:10.1038/srep27111. PMC 4890019. PMID 27251577.
Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.
Cabral, J.; Hugues, E.; Sporns, O.; Deco, G. (2011). "Role of local network oscillations in resting-state functional connectivity". NeuroImage. 57 (1): 130–139. doi:10.1016/j.neuroimage.2011.04.010. PMID 21511044. S2CID 13959959.
Hansel, D.; Mato, G.; Meunier, C (1993). "Clustering and slow switching in globally coupled phase oscillators" (PDF). Physical Review E. 48 (5): 3470–3477. Bibcode:1993PhRvE..48.3470H. doi:10.1103/physreve.48.3470. PMID 9961005.
Bick, C.; Timme, M.; Paulikat, D.; Rathlev, D.; Ashwin, P. (2011). "Chaos in Symmetric Phase Oscillator Networks". Physical Review Letters. 107 (24): 244101. arXiv:1105.2230. Bibcode:2011PhRvL.107x4101B. doi:10.1103/PhysRevLett.107.244101. PMID 22243002. S2CID 16144737.

ncbi.nlm.nih.gov

Bick, Christian; Goodfellow, Marc; Laing, Carlo R.; Martens, Erik A. (2020). "Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review". Journal of Mathematical Neuroscience. 10 (1): 9. arXiv:1902.05307. doi:10.1186/s13408-020-00086-9. PMC 7253574. PMID 32462281.
Breakspear M, Heitmann S, Daffertshofer A (2010). "Generative models of cortical oscillations: Neurobiological implications of the Kuramoto model". Front Hum Neurosci. 4 (190): 190. doi:10.3389/fnhum.2010.00190. PMC 2995481. PMID 21151358.
Forrester, D.M. (2015). "Arrays of coupled chemical oscillators". Scientific Reports. 5: 16994. arXiv:1606.01556. Bibcode:2015NatSR...516994F. doi:10.1038/srep16994. PMC 4652215. PMID 26582365.
Heitmann, S.; Gong, P.; Breakspear, M (2012). "A computational role for bistability and traveling waves in motor cortex". Front Comput Neurosci. 6 (67): 67. doi:10.3389/fncom.2012.00067. PMC 3438483. PMID 22973223.
Eom, Y.-H.; Boccaletti, S.; Caldarelli, G (2016). "Concurrent enhancement of percolation and synchronization in adaptive networks". Scientific Reports. 7: 015103. arXiv:1511.05468. Bibcode:2016NatSR...627111E. doi:10.1038/srep27111. PMC 4890019. PMID 27251577.

pitt.edu

math.pitt.edu

Pantaleone, James (October 2002). "Synchronization of metronomes" (PDF). American Journal of Physics. 70 (10): 992–1000. Bibcode:2002AmJPh..70..992P. doi:10.1119/1.1501118.

psu.edu

citeseerx.ist.psu.edu

Kazanci, F.; Ermentrout, B. (2006). "Pattern formation in an array of oscillators with electrical and chemical coupling". SIAM J Appl Math. 67 (2): 512–529. CiteSeerX 10.1.1.140.1020. doi:10.1137/060661041.

quantamagazine.org

Sloman, Leila (24 July 2023). "New Proof Shows That 'Expander' Graphs Synchronize". Quanta Magazine.

semanticscholar.org

api.semanticscholar.org

Strogatz, Steven H. (2000). "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators". Physica D. 143 (1–4): 1–20. Bibcode:2000PhyD..143....1S. doi:10.1016/S0167-2789(00)00094-4. S2CID 16668746. Retrieved 2024-01-04.
Witthaut, Dirk; Timme, Marc (2014). "Kuramoto Dynamics in Hamiltonian Systems". Phys. Rev. E. 90 (3): 032917. arXiv:1305.1742. Bibcode:2014PhRvE..90c2917W. doi:10.1103/PhysRevE.90.032917. PMID 25314514. S2CID 7510614.
Rodrigues, F. A.; Peron, T.K.; Jie, P.; Kurths, J. (2016). "The Kuramoto model in complex networks". Physics Reports. 610 (1): 1–98. arXiv:1511.07139. Bibcode:2016PhR...610....1R. doi:10.1016/j.physrep.2015.10.008. S2CID 119290926.
Abrams, D.M.; Strogatz, S.H. (2004). "Chimera states for coupled oscillators". Physical Review Letters. 93 (17): 174102. arXiv:nlin/0407045. Bibcode:2004PhRvL..93q4102A. doi:10.1103/physrevlett.93.174102. PMID 15525081. S2CID 8615112.
Heitmann, S.; Ermentrout, B. (2015). "Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity". Biological Cybernetics. 109 (3): 1–15. doi:10.1007/s00422-015-0646-6. PMID 25677527. S2CID 18561153.
Wiley, D.; Strogatz, S.; Girvan, M (2006). "The size of the sync basin". Chaos. 16 (1): 015103. Bibcode:2006Chaos..16a5103W. doi:10.1063/1.2165594. PMID 16599769. S2CID 21173189.
Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.
Ling, Shuyang; Xu, Ruitu; Bandeira, Afonso S. (January 2019). "On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization". SIAM Journal on Optimization. 29 (3): 1879–1907. arXiv:1809.11083. doi:10.1137/18M1217644. ISSN 1052-6234. S2CID 53067184.
Menara, T.; Baggio, G.; Bassett, D.; Pasqualetti, F. (2020). "Stability Conditions for Cluster Synchronizations in Networks of Heterogeneous Kuramoto Oscillators". IEEE Transactions on Control of Network Systems. 7 (1): 302–314. arXiv:1806.06083. doi:10.1109/TCNS.2019.2903914. S2CID 73729229.
Cabral, J.; Hugues, E.; Sporns, O.; Deco, G. (2011). "Role of local network oscillations in resting-state functional connectivity". NeuroImage. 57 (1): 130–139. doi:10.1016/j.neuroimage.2011.04.010. PMID 21511044. S2CID 13959959.
Hansel, D.; Mato, G.; Meunier, C (1993). "Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons". Europhysics Letters. 23 (5): 367–372. Bibcode:1993EL.....23..367H. doi:10.1209/0295-5075/23/5/011. S2CID 250884499.
Clusella, Pau; Politi, Antonio; Rosenblum, Michael (2016). "A minimal model of self-consistent partial synchrony". New Journal of Physics. 18 (9): 093037. arXiv:1607.07178. Bibcode:2016NJPh...18i3037C. doi:10.1088/1367-2630/18/9/093037. ISSN 1367-2630. S2CID 126227664.
Bick, C.; Timme, M.; Paulikat, D.; Rathlev, D.; Ashwin, P. (2011). "Chaos in Symmetric Phase Oscillator Networks". Physical Review Letters. 107 (24): 244101. arXiv:1105.2230. Bibcode:2011PhRvL.107x4101B. doi:10.1103/PhysRevLett.107.244101. PMID 22243002. S2CID 16144737.

siam.org

epubs.siam.org

Ling, Shuyang; Xu, Ruitu; Bandeira, Afonso S. (January 2019). "On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization". SIAM Journal on Optimization. 29 (3): 1879–1907. arXiv:1809.11083. doi:10.1137/18M1217644. ISSN 1052-6234. S2CID 53067184.

springer.com

link.springer.com

Strogatz, Steven H. (1994). "Norbert Wiener's Brain Waves". In Levin, Simon A. (ed.). Frontiers in Mathematical Biology. Lecture Notes in Biomathematics. Vol. 100. Berlin, Heidelberg: Springer. pp. 122–138. doi:10.1007/978-3-642-50124-1_7. ISBN 978-3-642-50124-1.

stevenstrogatz.com

Strogatz, Steven H. (2000). "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators". Physica D. 143 (1–4): 1–20. Bibcode:2000PhyD..143....1S. doi:10.1016/S0167-2789(00)00094-4. S2CID 16668746. Retrieved 2024-01-04.

uc3m.es

scala.uc3m.es

Acebrón, Juan A.; Bonilla, L. L.; Vicente, Pérez; Conrad, J.; Ritort, Félix; Spigler, Renato (2005). "The Kuramoto model: A simple paradigm for synchronization phenomena" (PDF). Reviews of Modern Physics. 77 (1): 137–185. Bibcode:2005RvMP...77..137A. doi:10.1103/RevModPhys.77.137. hdl:2445/12768.

worldcat.org

Maistrenko, Yuri L.; Popovych, Oleksandr V.; Tass, Peter A. (November 2005). "Chaotic Attractor in the Kuramoto Model". International Journal of Bifurcation and Chaos. 15 (11): 3457–3466. Bibcode:2005IJBC...15.3457M. doi:10.1142/S0218127405014155. ISSN 0218-1274.
Kassabov, Martin; Strogatz, Steven H.; Townsend, Alex (2021-07-01). "Sufficiently dense Kuramoto networks are globally synchronizing". Chaos: An Interdisciplinary Journal of Nonlinear Science. 31 (7): 073135. arXiv:2105.11406. Bibcode:2021Chaos..31g3135K. doi:10.1063/5.0057659. ISSN 1054-1500. PMID 34340322. S2CID 235166315.
Ling, Shuyang; Xu, Ruitu; Bandeira, Afonso S. (January 2019). "On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization". SIAM Journal on Optimization. 29 (3): 1879–1907. arXiv:1809.11083. doi:10.1137/18M1217644. ISSN 1052-6234. S2CID 53067184.
Clusella, Pau; Politi, Antonio; Rosenblum, Michael (2016). "A minimal model of self-consistent partial synchrony". New Journal of Physics. 18 (9): 093037. arXiv:1607.07178. Bibcode:2016NJPh...18i3037C. doi:10.1088/1367-2630/18/9/093037. ISSN 1367-2630. S2CID 126227664.

worldscientific.com

Maistrenko, Yuri L.; Popovych, Oleksandr V.; Tass, Peter A. (November 2005). "Chaotic Attractor in the Kuramoto Model". International Journal of Bifurcation and Chaos. 15 (11): 3457–3466. Bibcode:2005IJBC...15.3457M. doi:10.1142/S0218127405014155. ISSN 0218-1274.