Kuramoto model

The Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto (蔵本 由紀, Kuramoto Yoshiki),[1][2] is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators.[3][4] Its formulation was motivated by the behavior of systems of chemical and biological oscillators, and it has found widespread applications in areas such as neuroscience[5][6][7][8] and oscillating flame dynamics.[9][10] Kuramoto was quite surprised when the behavior of some physical systems, namely coupled arrays of Josephson junctions, followed his model.[11]

The model makes several assumptions, including that there is weak coupling, that the oscillators are identical or nearly identical, and that interactions depend sinusoidally on the phase difference between each pair of objects.

  1. ^ Kuramoto, Yoshiki (1975). H. Araki (ed.). Lecture Notes in Physics, International Symposium on Mathematical Problems in Theoretical Physics. Vol. 39. Springer-Verlag, New York. p. 420.
  2. ^ Kuramoto Y (1984). Chemical Oscillations, Waves, and Turbulence. New York, NY: Springer-Verlag.
  3. ^ 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ 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.
  7. ^ 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.
  8. ^ 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.
  9. ^ Sivashinsky, G.I. (1977). "Diffusional-thermal theory of cellular flames". Combust. Sci. Technol. 15 (3–4): 137–146. doi:10.1080/00102207708946779.
  10. ^ 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.
  11. ^ Steven Strogatz, Sync: The Emerging Science of Spontaneous Order, Hyperion, 2003.