Universality in the one-dimensional chain of phase-coupled oscillators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 4, 2009, Pages

  Lee, Tony E ^a   Refael, G ^a   Cross, M C ^a   Kogan, Oleg ^b   Rogers, Jeffrey L ^c,d  

^a California Institute of Technology   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d DEFENSE ADVANCED RESEARCH PROJECTS AGENCY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION LENGTH SCALE; COUPLING DISTRIBUTION; CRITICAL EXPONENT; FIXED POINTS; LONG TAIL; LOW FREQUENCY; NUMERICAL SIMULATION; ONE-DIMENSIONAL CHAINS; PHASE-COUPLED OSCILLATORS; RANDOMLY DISTRIBUTED; RENORMALIZATION GROUP; SYNCHRONIZED CLUSTERS; UNIVERSAL APPROACH; UNIVERSAL SCALING; UNIVERSALITY CLASS; WEAK RANDOMNESS;

COMPUTER SIMULATION; OSCILLATORS (MECHANICAL);

OSCILLATORS (ELECTRONIC);

EID: 70449429480     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.046210     Document Type: Article

References (20)

1. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
2. A. S. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, New York, 2001).
3. J. A. Acebrón, L. L. Bonilla, C. J. P. Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005). 10.1103/RevModPhys.77.137
4. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. 76, 404 (1996). 10.1103/PhysRevLett.76.404
5. A. G. Vladimirov, G. Kozyreff, and P. Mandel, Europhys. Lett. 61, 613 (2003). 10.1209/epl/i2003-00115-8
6. F. Varela, J.-P. Lachaux, E. Rodriguez, and J. Martinerie, Nat. Rev. Neurosci. 2, 229 (2001). 10.1038/35067550
7. Z. Néda, E. Ravasz, Y. Brechet, T. Vicsek, and A.-L. Barabási, Nature (London) 403, 849 (2000). 10.1038/35002660
8. H. Hong, H. Park, and M. Y. Choi, Phys. Rev. E 72, 036217 (2005). 10.1103/PhysRevE.72.036217
9. H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007). 10.1103/PhysRevLett.99.184101
10. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Westview Press, Boulder, CO, 1992).
11. H. Sakaguchi, S. Shinomoto, and Y. Kuramoto, Prog. Theor. Phys. 77, 1005 (1987). 10.1143/PTP.77.1005
12. H. Daido, Phys. Rev. Lett. 61, 231 (1988). 10.1103/PhysRevLett.61.231
13. S. H. Strogatz and R. E. Mirollo, J. Phys. A 21, L699 (1988). 10.1088/0305-4470/21/13/005
14. O. Kogan, J. L. Rogers, M. C. Cross, and G. Refael, Phys. Rev. E 80, 036206 (2009). 10.1103/PhysRevE.80.036206
15. O. Kogan, Ph.D. thesis, California Institute of Technology, 2008.
16. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992).
17. D. S. Fisher, Phys. Rev. B 50, 3799 (1994). 10.1103/PhysRevB.50.3799
18. S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997). 10.1103/RevModPhys.69.315
19. J. Ochab and P. F. Góra, e-print arXiv:0909.0043.
20. By the definition of a center, | Δω | <2E. When a center gets checked for strong coupling decimation, K =E. Thus, r=2 K/ | Δω | >1. Hence, when a center is checked for strong coupling decimation, it will always be decimated as such.