Conformists and contrarians in a Kuramoto model with identical natural frequencies

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

Volumn 84, Issue 4, 2011, Pages

  Hong, Hyunsuk ^a   Strogatz, Steven H ^b  

^a Chonbuk National University   (South Korea)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIPHASE; EXACT SOLUTION; IN-PHASE; KURAMOTO MODELS; MEAN FIELD; RICH DYNAMICS; TRAVELING WAVE;

DISPLAY DEVICES; NATURAL FREQUENCIES;

MICROWAVE OSCILLATORS;

EID: 80054852668     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.046202     Document Type: Article

References (55)

1. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, New York, 1984).
2. J. W. Swift, S. H. Strogatz, and K. Wiesenfeld, Physica D PDNPDT 0167-2789 10.1016/0167-2789(92)90057-T 55, 239 (1992);
3. K. Wiesenfeld, Physica B PHYBE3 0921-4526 10.1016/0921-4526(96)85057-5 222, 315 (1996); (Pubitemid 126370075)
4. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.404 76, 404 (1996);
5. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.57.1563 57, 1563 (1998);
6. K. Park and M. Y. Choi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.56.387 56, 387 (1997);
7. G. Filatrella, N. F. Pedersen, and K. Wiesenfeld, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.2513 61, 2513 (2000);
8. B. C. Daniels, S. T. M. Dissanayake, and B. R. Trees, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.67.026216 67, 026216 (2003).
9. G. Grüner and A. Zettl, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(85)90073-0 119, 117 (1985);
10. G. Grüner, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.60. 1129 60, 1129 (1988);
11. S. H. Strogatz and R. E. Mirollo, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/21/13/005 21, L699 (1988);
12. S. H. Strogatz and R. E. Mirollo, Physica D PDNPDT 0167-2789 10.1016/0167-2789(88)90074-7 31, 143 (1989);
13. C. M. Marcus, S. H. Strogatz, and R. M. Westervelt, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.5588 40, 5588 (1989).
14. Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.1500 52, 1500 (1995);
15. S. Y. Kourtchatov, V. V. Likhanskii, A. P. Napartovich, F. T. Arecchi, and A. Lapucci, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.4089 52, 4089 (1995);
16. G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3809 85, 3809 (2000); (Pubitemid 32027189)
17. G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.64.016613 64, 016613 (2001);
18. R. A. Oliva and S. H. Strogatz, Int. J. Bifurcation Chaos IJBEE4 0218-1274 10.1142/S0218127401003450 11, 2359 (2001);
19. A. G. Vladimirov, G. Kozyreff, and P. Mandel, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00115-8 61, 613 (2003). (Pubitemid 36316705)
20. C. von Cube, S. Slama, D. Kruse, C. Zimmermann, P. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.083601 93, 083601 (2004);
21. J. Javaloyes, M. Perrin, and A. Politi, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.78.011108 78, 011108 (2008).
22. G. Russo and P. Smereka, SIAM. J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139993260563 56, 327 (1996).
23. J. Pantaleone, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.58.073002 58, 073002 (1998).
24. N. Mazouz, K. Krischer, G. Flätgen, and G. Ertl, J. Phys. Chem. B JPCBFK 1520-6106 10.1021/jp962659q 101, 2403 (1997);
25. I. Z. Kiss, W. Wang, and J. L. Hudson, Chaos CHAOEH 1054-1500 10.1063/1.1426382 12, 252 (2002);
26. M. Wickramasinghe and I. Z. Kiss, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.83.016210 83, 016210 (2011).
27. Z. Néda, E. Ravasz, Y. Brechet, T. Vicsek, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/35002660 403, 849 (2000); (Pubitemid 30130975)
28. Z. Néda, E. Ravasz, T. Vicsek, Y. Brechet, and A.-L. Barabási, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.6987 61, 6987 (2000).
29. A. T. Winfree, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(67) 90051-3 16, 15 (1967);
30. A. T. Winfree, The Geometry of Biological Time (Springer, New York, 1980).
31. H. Daido, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.1073 68, 1073 (1992).
32. H. Daido, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.2145 61, 2145 (2000);
33. J. C. Stiller and G. Radons, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.58.1789 58, 1789 (1998).
34. H. Daido, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.77.622 77, 622 (1987);
35. L. L. Bonilla, C. J. P. Vicente, and J. M. Rubi, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01053600 70, 921 (1993);
36. D. H. Zanette, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10238-4 72, 190 (2005). (Pubitemid 41525275)
37. H. Hong and S. H. Strogatz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.054102 106, 054102 (2011).
38. S. A. Marvel and S. H. Strogatz, Chaos CHAOEH 1054-1500 10.1063/1.3087132 19, 013132 (2009).
39. E. Ott and T. M. Antonsen, Chaos CHAOEH 1054-1500 10.1063/1.2930766 18, 037113 (2008);
40. E. Ott and T. M. Antonsen, Chaos CHAOEH 1054-1500 10.1063/1.3136851 19, 023117 (2009).
41. E. A. Rogers, R. Kalra, R. D. Schroll, A. Uchida, D. P. Lathrop, and R. Roy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.084101 93, 084101 (2004).
42. P. L. Krapivsky and S. Redner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.238701 90, 238701 (2003);
43. S. Galam, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.10.041 333, 453 (2004);
44. M. S. Lama, J. M. López, and H. S. Wio, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10299-3 72, 851 (2005). (Pubitemid 41757782)
45. K. Binmore, The Breakdown of Social Contracts, in Social Dynamics, edited by, S. N. Durlauf, and, H. Peyton Young, (MIT Press, Cambridge, MA, 2004).
46. L. S. Tsimring, N. F. Rulkov, M. L. Larsen, and M. Gabbay, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.014101 95, 014101 (2005). (Pubitemid 41506365)
47. S. Watanabe and S. H. Strogatz, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90196-1 74, 197 (1994).
48. A. Pikovsky and M. Rosenblum, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.264103 101, 264103 (2008).
49. S. A. Marvel, R. E. Mirollo, and S. H. Strogatz, Chaos CHAOEH 1054-1500 10.1063/1.3247089 19, 043104 (2009).
50. E. A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So, and T. M. Antonsen, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.79.026204 79, 026204 (2009).
51. L. M. Childs and S. H. Strogatz, Chaos CHAOEH 1054-1500 10.1063/1.3049136 18, 043128 (2008).
52. C. R. Laing, Chaos CHAOEH 1054-1500 10.1063/1.3068353 19, 013113 (2009);
53. C. R. Laing, Physica D PDNPDT 0167-2789 10.1016/j.physd.2009.04.012 238, 1569 (2009);
54. C. R. Laing, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.81.066221 81, 066221 (2010).
55. S. A. Marvel, H. Hong, and S. H. Strogatz (to be published).