No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Synchronization transition of identical phase oscillators in a directed small-world network
1.G. V. Osipov, J. Kurths, and C. Zhou, Synchronization in Oscillatory Networks, Springer Series in Synergetics (Springer, Berlin, 2007).
2.A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization : A Universal Concept in Nonlinear Sciences, Cambridge Nonlinear Science Series Vol. 12 (Cambridge University Press, Cambridge, England, 2001).
3.A. T. Winfree, The Geometry of Biological Time, Interdisciplinary Applied Mathematics Vol. 12, 2nd ed. (Springer-Verlag, New York, 2001).
4.Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics Vol. 19 (Springer-Verlag, Berlin, 1984).
5.A. Díaz-Guilera and A. Arenas, Bio-Inspired Computing and Communication (Springer-Verlag, Berlin, 2008), p. 184.
8.Y. Kuramoto, International Symposium on Mathematical Problems in Theoretical Physics, Kyoto University, Kyoto, 1975, Lecture Notes in Physics Vol. 39 (Springer, Berlin, 1975), pp. 420–422.
10.E. Ott and T. M. Antonsen, Chaos 18, 6 (2008).
25.Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002).
32.H. Risken, The Fokker-Planck Equation, Methods of Solution and Applications, Springer Series in Synergetics Vol. 18, 2nd ed. (Springer-Verlag, Berlin, 1989).
Article metrics loading...
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on the shortcut density and on the asymmetry of the phase coupling function, there exists a regime of persistent chaotic dynamics. By increasing the density of shortcuts or decreasing the asymmetry of the phase coupling function, we observe a discontinuous transition in the ability of the system to synchronize. Using a control technique, we identify the bifurcation scenario of the order parameter. We also discuss the relation between dynamics and topology and remark on the similarity of the synchronization transition to directed percolation.
Full text loading...
Most read this month