Mean field and cavity analysis for coupled oscillator networks

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

Volumn 78, Issue 3, 2008, Pages

  Hatchett, Jonathan P L ^a   Uezu, Tatsuya ^b  

^a Nara Women's University ^*  (United Kingdom)

^b NARA WOMEN'S UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; MECHANICS; MONTE CARLO METHODS; OSCILLATORS (MECHANICAL); PARAMETER ESTIMATION; PHASE DIAGRAMS; SPEED; SPIN DYNAMICS; STATISTICAL MECHANICS;

CONNECTED NETWORKS; COUPLED OSCILLATOR NETWORKS; COUPLED OSCILLATORS; EQUILIBRIUM STATISTICAL MECHANICS; FERRO-MAGNETIC INTERACTIONS; HAMILTONIAN; MEAN FIELDS; MONTE-CARLO SIMULATIONS; ORDER PARAMETERS; ORDERED PHASE; OSCILLATOR NETWORKS; RANDOM GRAPHS; SPIN SYSTEMS;

FLOW INTERACTIONS;

EID: 51849110994     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.036106     Document Type: Article

References (26)

1. S. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
2. Handbook of Graphs and Networks: From the Genome to the Internet, edited by, S. Bornholdt, and, H. Schuster, (Wiley-VCH, New York, 2002).
3. M. E. J. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003).
4. B. Bollobás, Modern Graph Theory (Springer, New York, 1998).
5. D. Watts and S. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
6. R. A. Z. O. H. Jeong, B. Tombor, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/35036627 407, 651 (2000).
7. T. Uezu, C. Kadono, J. P. L. Hatchett, and A. C. C. Coolen, Prog. Theor. Phys. Suppl. PTPSEP 0375-9687 161, 385 (2006).
8. B. Wemmenhove and A. Coolen, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/37/302 36, 9617 (2003).
9. R. Vicente, D. Saad, and Y. Kabashima, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.5352 60, 5352 (1999).
10. A. Hartmann and M. Weigt, Phase Transitions in Combinatorial Optimization Problems (Wiley-VCH, Berlin, 2006).
11. M. Mézard, G. Parisi, and R. Zecchina, Science SCIEAS 0036-8075 10.1126/science.1073287 297, 812 (2002).
12. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
13. J. A. Acebrón, L. L. Bonilla, C. J. Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77.137 77, 137 (2005).
14. A. Arenas, A. Diaz-Guilera, and C. J. Perez-Vicente, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.114102 96, 114102 (2006).
15. B. J. Kim, H. Hong, P. Holme, G. S. Jeon, P. Minnhagen, and M. Y. Choi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056135 64, 056135 (2001).
16. H. Hong, M. Y. Choi, and B. J. Kim, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.047104 65, 047104 (2002).
17. N. S. Skantzos, I. P. Castillo, and J. P. L. Hatchett, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.066127 72, 066127 (2005).
18. A. C. C. Coolen, N. S. Skantzos, I. P. Castillo, C. J. Perez-Vicente, J. P. L. Hatchett, B. Wemmenhove, and T. Nikoletopoulos, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/39/001 38, 8289 (2005).
19. T. Ichinomiya, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.016109 72, 016109 (2005).
20. P. C. Matrin, E. Siggia, and H. Rose, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.8.423 8, 423 (1973).
21. C. DeDominicis, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.18.4913 18, 4913 (1978).
22. S. Kirkpatrick and D. Sherrington, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.17.4384 17, 4384 (1978).
23. A. C. C. Coolen and C. J. Perez-Vicente, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/16/301 36, 4477 (2003).
24. M. Mézard, G. Parisi, and M. Virasoro, Spin-Glass Theory and Beyond (World Scientific, Singapore, 1987).
25. J. Hatchett and T. Uezu, Proceedings of the 2007 IEEE Symposium Series on Computational Intelligence (FOCI'07), 2007, p. 169.
26. H. Daido, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.1073 68, 1073 (1992).