ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kasatkin D. V., Nekorkin V. I. Dynamics of a network of interacting phase oscillators with dynamic couplings. Izvestiya VUZ. Applied Nonlinear Dynamics, 2015, vol. 23, iss. 4, pp. 58-70. DOI: 10.18500/0869-6632-2015-23-4-58-70

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 109)
Article type: 

Dynamics of a network of interacting phase oscillators with dynamic couplings

Kasatkin Dmitry Vladimirovich, Institute of Applied Physics of the Russian Academy of Sciences
Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences

We investigate dynamical states formed in a network of coupled phase oscillators in which strength of interactions between oscillators evolve dynamically depending on their relative phases. The feature of the system is co-evolution of coupling weights and states of elements. It is ascertained that depending on the parameters the network exhibit several types of behavior: globally synchronized state, two-cluster and multi-cluster states, various synchronized states with a fixed phase relationship between oscillators and desynchronized state.

  1. Kuramoto Y. Chemical Oscillations, Waves, and Turbulence. Berlin: Springer, 1984. 158 p.
  2. Strogatz S.H. Exploring complex networks // Nature. 2001. Vol. 410. P. 268–276.
  3. Dorfler F., Bullo F. Synchronization in complex networks of phase oscillators: A survey // Automatica. 2014. Vol. 50. P. 1539–1564.
  4. Acebron J.A., Bonilla L.L., Perez Vicente C.J., Ritort F. and Spigler R. The Kuramoto model: A simple paradigm for synchronization phenomena // Reviews of Modern Physics. 2005. Vol. 77, № 1. P. 137.
  5. Pikovsky A., Rosenblum M. Dynamics of globally coupled oscillators: Progress and perspectives // Chaos. 2015. Vol. 25, № 9. P. 097616.
  6. Gomes-Gardenes J., Moreno Y., Arenas A. Synchronizability determined by coupling strengths and topology on complex networks // Physical Review E. 2007. Vol. 75, № 6. P. 066106.
  7. Stout J., Whiteway M., Ott E., Girvan M., Antonsen T.M. Local synchronization in complex networks of coupled oscillators // Chaos. 2011. Vol. 21, № 2. P. 025109.
  8. Strogatz S.H., Mirollo R.E. Stability of incoherence in a population of coupled oscillators // J. of Statistical Physics. 1991. Vol. 63, № 3-4. P. 613.
  9. Brede M. Synchronizability determined by coupling strengths and topology on complex networks // Physics Letters A. 2008. Vol. 372, № 15. P. 2618.
  10. Hong H., Strogatz S.H. Kuramoto model of coupled oscillators with positive and negative coupling parameters: An example of conformist and contrarian oscillators // Physical Review Letters. 2011. Vol. 106, № 5. P. 054102.
  11. Kloumann I.M., Lizarraga I.M., Strogatz S.H. Phase diagram for the Kuramoto model with van Hemmen interactions // Physical Review E. 2014. Vol. 89, № 1. P. 012904.
  12. Earl M.G., Strogatz S.H. Synchronization in oscillator networks with delayed coupling: A stability criterion // Physical Review E. 2003. Vol. 67, № 3. P. 036204.
  13. Nordenfelt A., Wagemakers A., Sanjuan M.A.F. Frequency dispersion in the time-delayed Kuramoto model // Physical Review E. 2014. Vol. 89, № 3. P. 032905.
  14. Aoki T., Aoyagi T. Self-organized network of phase oscillators coupled by activity-dependent interactions // Physical Review E. 2011. Vol. 84, № 6. P. 066109.
  15. Gutierrez R., Amann A., Assenza S., Gomes-Gardenes J., Latora V., Boccaletti S. Emerging meso- and macroscales from synchronization of adaptive networks // Physical Review Letters. 2011. Vol. 107, № 23. P. 234103.
  16. Assenza S., Gutierrez R., Gomes-Gardenes J., Latora V., Boccaletti S. Emergence of structural patterns out of synchronization in networks with competitive interactions // Scientific Reports. 2011. Vol. 1. P. 1–8.
  17. Chandrasekar V.K., Sheeba J.H., Subash B., Lakshmanan M., Kurths J. Adaptive coupling induced multi-stable states in complex networks // Physica D. 2014. Vol. 267. P. 36.
  18. Ren Q., He M., Yu X., Long Q, Zhao J. The adaptive coupling scheme and heterogeneity in intrinsic frequency and degree distributions of the complex networks // Physics Letters A. 2014. V. 378, № 3. P. 139.
  19. Kasatkin D.V., Nekorkin V.I. Dynamics of phase oscillators with plastic couplings // Radiophysics and Quantum Electronics. 2015. (in press)
Short text (in English):
(downloads: 63)