Abstract
At how long of an interaction range does an oscillator system behave as a fully-connected one? To answer this question, we consider a system of nonlocally-coupled phase oscillators in one dimension, and explore the effects of a variable interaction range L on collective dynamics. In particular, we investigate the winding-number distribution, paying particular attention to the existence of a twisted wave in the system, and observe that the twisted state vanishes when the interaction range exceeds a critical value. Finite-size scaling of the width of the winding-number distribution reveals that the transition occurs at 2L/N ≈ 0.6, regardless of the system size N. We also show that at the same transition point for the topological twisted state, the phase synchrony in the system becomes partial.
Similar content being viewed by others
References
A. T. Winfree, The Geometry of Biological Time (Springer, New York, 1980); Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984); J. A. Acebron, L. L. Bonilla, C. J. P. Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005); see also the references therein.
H. Daido, Prog. Theor. Phys. 77, 622 (1987); Phys. Rev. Lett. 68, 1073 (1992); L. L. Bonilla, C. J. P. Vicente, and J. M. Rubi, J. Stat. Phys. 70, 921 (1993); D. H. Zanette, Europhys. Lett. 72, 190 (2005).
H. Hong and S. H. Strogatz, Phys. Rev. Lett. 106, 054102 (2011).
E. A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So, and T. M. Antonsen, Phys. Rev. E 79, 026204 (2009).
D. A. Wiley, S. H. Strogatz, and M. Girvan, Chaos 16, 015103 (2006).
L. S. Tsimring, N. F. Rulkov, M. L. Larsen, and M. Gabbay, Phys. Rev. Lett. 95, 014101 (2005); T. Girnyk, M. Hasler, and Y. Maistrenko, Chaos 22, 013114 (2012).
J. M. Kosterlitz, J. Phys. C: Solid State Phys. 7, 1046 (1974); J. M. Kosterlitz and D. J. Thouless, ibid. 6, 1181 (1974).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hong, H., Kim, B.J. Winding-number excitation in one-dimensional oscillators with variable interaction range. Journal of the Korean Physical Society 64, 954–957 (2014). https://doi.org/10.3938/jkps.64.954
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.64.954