Dynamics of a large ring of coupled active and inactive oscillators

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

Volumn 83, Issue 2, 2011, Pages

  Daido, Hiroaki ^a  

^a Osaka Prefecture University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACCIDENTAL DAMAGE; COUPLED OSCILLATORS; CRITICAL RATIO; GLOBAL COUPLING; PHASE COHERENCE; QUENCHED DISORDER; RANDOM ASSIGNMENT; SYSTEM SIZE;

OSCILLATORS (MECHANICAL);

OSCILLATORS (ELECTRONIC);

EID: 79952553559     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.026209     Document Type: Article

References (30)

1. A. T. Winfree, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(67) 90051-3 16, 15 (1967).
2. A. T. Winfree, The Geometry of Biological Time (Springer, New York, 2001).
3. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
4. S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/35065725 410, 268 (2001). (Pubitemid 32216604)
5. J. A. Acebrón, L. L. Bonilla, C. J. P. Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77.137 77, 137 (2005). (Pubitemid 41490657)
6. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization-A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, UK, 2001).
7. I. Z. Kiss, Y. Zhai, and J. L. Hudson, Science SCIEAS 0036-8075 10.1126/science.1070757 296, 1676 (2002). (Pubitemid 34579162)
8. C. Liu, D. R. Weaver, S. H. Strogatz, and S. M. Reppert, Cell CELLB5 0092-8674 10.1016/S0092-8674(00)80473-0 91, 855 (1997). (Pubitemid 28007741)
9. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.404 76, 404 (1996).
10. S. J. Aton and E. D. Herzog, Neuron NERNET 0896-6273 10.1016/j.neuron. 2005.11.001 48, 531 (2005). (Pubitemid 41654674)
11. J. Miake, E. Marbán, and H. B. Nuss, Nature (London) NATUAS 0028-0836 10.1038/419132b 419, 132 (2002).
12. H. Daido and K. Nakanishi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.104101 93, 104101 (2004).
13. K. Nakanishi and H. Daido, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.161.173 161, 173 (2006). (Pubitemid 43925681)
14. H. Daido and K. Nakanishi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.056206 75, 056206 (2007); (Pubitemid 47001018)
15. H. Daido and K. Nakanishi, Phys. Rev. E PTPSAL 1539-3755 10.1103/PhysRevE.76.049901 76, 049901 (E) (2007). (Pubitemid 47631526)
16. D. Pazó and E. Montbrió, Phys. Rev. E PTPSAL 1539-3755 10.1103/PhysRevE.73.055202 73, 055202 (2006). (Pubitemid 43829530)
17. G. Tanaka, Y. Okada, and K. Aihara, Phys. Rev. E PTPSAL 1539-3755 10.1103/PhysRevE.82.035202 82, 035202 (R) (2010).
18. H. Daido, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/84/10002 84, 10002 (2008).
19. J. Yang, Phys. Rev. E EULEEJ 1539-3755 10.1103/PhysRevE.76.016204 76, 016204 (2007). (Pubitemid 47153006)
20. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).
21. This conjecture will be valid for higher-dimensional systems of locally coupled oscillators as well by the same reasoning. In fact, our numerical results for a two-dimensional system support this.
22. To be precise, except when it happens to be an integer multiple of 1 / N, the right-hand side of Eq. (5) should be interpreted as 1 2 (M N + M + 1 N), where M is the integer satisfying M N < a a + b < M + 1 N.
23. 2 > 0, if the continuum limit is taken [3].
24. H. Daido, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/87/40001 87, 40001 (2009).
25. J. D. Murray, Mathematical Biology (Springer, Berlin, 1993).
26. Y. Ibata, M. Tanaka, Y. Tamada, S. Hayashi, F. Kawakami, T. Takamatsu, Y. Hisa, and H. Okamura, Neuroscientist EULEEJ 1073-8584 10.1177/ 107385849700300409 3, 215 (1997).
27. Y. Braiman, W. L. Ditto, K. Wiesenfeld, and M. L. Spano, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95)00570-S 206, 54 (1995).
28. H. Fukuda, N. Nakamichi, M. Hisatsune, H. Murase, and T. Mizuno, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.098102 99, 098102 (2007). (Pubitemid 47357780)
29. W. Chen, S. C. Chen, E. Avalos, O. Drugova, G. Osipov, P.-Y. Lai, and C. K. Chan, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/86/18001 86, 18001 (2009).
30. H. Daido (submitted).