We consider a network of Kuramoto phase oscillators with randomly blinking couplings. Applicability of the averaging method for small switching intervals is rigorously substantiated. Using this method, we analytically estimate the threshold coupling force for synchronizing the ensemble oscillators. The threshold synchronization is studied as a function of the switching interval for various network sizes. The effect of preserving synchronization for a significant increase in the switching interval is found, which is the key feature of the system since a slight increase in this interval usually leads to the synchronization failure. The intermittent-synchronization possibility for small network sizes and large switching intervals is shown. An increase in the network size is shown to result in a stability increase due to the decreasing probability of appearance of uncoupled configurations. The regions corresponding to the global synchronization of oscillators are singled out in the system-parameter space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Y.Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer, Berlin (1984).
D.C. Michaels, E.P.Matyas, and J. Jalife, Circ. Res., 61, No. 5, 704 (1987).
E. Brown, P. Holmes, and J.Moehlis, “Globally coupled oscillator networks,” in: E.Kaplan, J.E. Marsden, and K.R. Sreenivasan, eds., Perspectives and Problems in Nonlinear Science: a Celebratory Volume in Honor of Larry Sirovich, Springer, New York (2003), p. 183.
K. Wiesenfeldt, P.Colet, and S. Strogatz, Phys. Rev. E, 57, No. 2, 1563 (1998).
K.G.Mishagin, V.D. Shalfeev, and V.P. Ponomarenko, Nonlinear Dynamics of the Systems for Phasing in Antenna Arrays [in Russian], Nizhny Novgorod Univ., Nizhny Novgorod (2007).
Z. Neda, E.Ravasz, T. Vicsek, et al., Phys. Rev. E, 61, No. 6, 6987 (2000).
S. H. Strogatz, D. M. Abrams, A.McRobie, et al., Nature, 438, No. 7064, 43 (2005).
F. Dorfler and F.Bullo, Automatica, 50, No. 6, 1539 (2014).
I. V. Belykh, V.N. Belykh, and M. Hasler, Physica D, 195, Nos. 1–2, 188 (2004).
D. L. Mills, IEEE Trans. Commun., 39, No. 10, 1482 (1991).
A. S.Dmitriev, M. E.Gerasimov, R. Yu. Emel’yanov, and V. V. Itskov, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Din., 23, No. 2, 21 (2015).
Y.Kuramoto, “Self-entrainment of a population of coupled non-linear oscillators,” in: H.Araki, ed., Int. Symp. on Mathematical Problems in Theoretical Physics, Kyoto Univ., Kyoto, January 23–29, 1975, Lect. Notes Phys., Vol. 39, Springer, New York (1975), p. 420.
V. N. Belykh, V. S.Petrov, and G.V.Osipov, Regul. Chaot. Dyn., 20, No. 1, 37 (2015).
N. N. Bogolyubov and Yu. A. Mitropol’sky, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Gostekhizdat, Moscow (1955).
A. Skorokhod, F.Hoppensteadt, and H. Salehi, Random Perturbation Methods, Springer-Verlag, New York (2002).
R. Z.Khas’minsky, Stability of the Systems of Differential Equations under Random Perturbations of their Parameters [in Russian], Nauka, Moscow (1969).
S. H. Strogatz, Physica D, 143, Nos. 1–4, 1 (2000).
M. Hasler, V.N. Belykh, and I. Belykh, SIAM J. Appl. Dyn. Syst., 12, No. 2, 1007 (2013).
M. Hasler, V.N. Belykh, and I. Belykh, SIAM J. Appl. Dyn. Sys., 12, No. 2, 1031 (2013).
I. Belykh, V. Belykh, M.Hasler, and R. Jeter, Eur. Phys. J. Spec. Topics, 222, No. 10, 2497 (2013).
M.Porfiri, D. J. Stilwell, E. M. Bollt, and J. D. Skufca, Physica D, 224, 102 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 60, No. 9, pp. 851–858, September 2017.
Rights and permissions
About this article
Cite this article
Barabash, N.V., Belykh, V.N. Synchronization Thresholds in an Ensemble of Kuramoto Phase Oscillators with Randomly Blinking Couplings. Radiophys Quantum El 60, 761–768 (2018). https://doi.org/10.1007/s11141-018-9844-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-018-9844-0