Low dimensional behavior of large systems of globally coupled oscillators

Chaos

Volumn 18, Issue 3, 2008, Pages

  Ott, Edward ^a   Antonsen, Thomas M ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749126999     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2930766     Document Type: Article

References (22)

1. A. Pikovsky, M. Rosenblum, and J. Kürths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001); S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order (Penguin Science, New York, 2004); S. Boccaletti, J. Kürths, G. Osipov, D. L. Valladeres, and C. S. Zhou, Phys. Rep. 366, 1 (2002).
2. S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, and H. Okamura, Science 302, 1408 (2003).
3. I. Z. Kiss, Y. Zhai, and J. L. Hudson, Science 296, 1676 (2005).
4. K. Wiesenfeld and J. W. Swift, Phys. Rev. E 51, 1020 (1995).
5. J. Pantaleone, Phys. Rev. D 58, 073002 (1998).
6. R. Häubler, R. Bartussek, and P. Hänggi, AIP Conf. Proc. 411, 243 (1997).
7. Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, edited by, H. Araki, (Springer-Verlag, Berlin, 1975), Vol. 39; Chemical Oscillations, Waves and Turbulence (Springer, New York, 1984).
8. For reviews of the Kuramoto model, see E. Ott, Chaos in Dynamical Systems, 2nd ed. (Cambridge University Press, Cambridge, 2002), Chap.; S. H. Strogatz, Physica D 0167-2789 10.1016/S0167-2789(00)00094-4 143, 1 (2000); J. A. Acebron, L. L. Bonilla, C. J. P. Vincente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
9. H. Sakaguchi, Prog. Theor. Phys. 0033-068X 10.1143/PTP.79.39 79, 39 (1988); H. Kori and A. S. Mikhailov, Phys. Rev. E 74, 066115 (2006).
10. T. M. Antonsen, Jr., R. Faghih, M. Girvan, E. Ott, and J. Platig, Chaos 18, 037112 (2008) (this issue).
11. E. Barreto, B. Hunt, E. Ott, and P. So, Phys. Rev. E 77, 036107 (2008).
12. E. Montbrio, J. Kürths, and B. Blasius, Phys. Rev. E 70, 056125 (2004).
13. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955), Theorem 8.4 of Chap..
14. R. Mirollo and S. H. Strogatz, J. Nonlinear Sci. 17, 309 (2007).
15. S. H. Strogatz, R. E. Mirollo, and P. C. Matthews, Phys. Rev. Lett. 68, 2730 (1992).
16. E. Niebur, H. G. Schuster, and D. M. Kammen, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.67.2753 67, 2753 (1991); S. Kim, S. H. Park, and C. S. Ryu, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.79.2911 79, 2911 (1997); H. Kori and Y. Kuramoto, Phys. Rev. E 1063-651X 10.1103/PhysRevE.63.046214 63, 046214 (2001); E. Montbrió, D. Pazo, and J. Schmidt, Phys. Rev. E 74, 056201 (2006).
17. M. K. S. Yeung and S. H. Strogatz, Phys. Rev. Lett. 82, 648 (1999); to put Eq. in the notation of this reference, make the replacement s+i ω0 →s.
18. M. Choi, H. J. Kim, D. Kim, and H. Hong, Phys. Rev. E 61, 371 (2000).
19. B. Eckhardt, E. Ott, S. H. Strogatz, D. M. Abrams, and A. McRobie, Phys. Rev. E 75, 021110 (2007).
20. Y. Kuramoto and I. Nishikawa, J. Stat. Phys. 49, 569 (1986).
21. J. D. Crawford, J. Stat. Phys. 74, 1047 (1994).
22. S. Watanabe and S. H. Strogatz, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.70.2391 70, 2391 (1993); S. Watanabe and S. H. Strogatz, Physica D 74, 197 (1994).