Echo phenomena in large systems of coupled oscillators

Chaos

Volumn 18, Issue 3, 2008, Pages

  Ott, Edward ^a   Platig, John H ^a   Antonsen, Thomas M ^a   Girvan, Michelle ^a  

^a University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749138454     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2973816     Document Type: Article

References (19)

1. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
2. S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order (Penguin Science, New York, 2004).
3. J. Buck, Q. Rev. Biol. 63, 265 (1988).
4. T. J. Walker, Science 166, 891 (1969).
5. D. C. Michaels, Circ. Res. 61, 704 (1987).
6. W. Singer, Annu. Rev. Physiol. 0066-4278 10.1146/annurev.physiol.55.1.349 55, 349 (1993); R. Eckhorn, R. Bauer, W. Jordan, M. Brosch, W. Kruse, M. Munk, and H. J. Reitboeck, Biol. Cybern. 0340-1200 10.1007/BF00202899 60, 121 (1988); C. M. Gray, Nature (London) 338, 334 (1989).
7. S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, and H. Okamura, Science 0036-8075 10.1126/science.1089287 302, 1408 (2003); T. M. Antonsen, R. T. Faghih, M. Girvan, E. Ott, and J. Platig, Chaos 18, 037112 (2008).
8. I. Z. Kiss, Y. Zhai, and J. L. Hudson, Science 296, 1676 (2005).
9. K. Wiesenfeld and J. W. Swift, Phys. Rev. E 51, 1020 (1995).
10. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984); Y. Kuramoto, International Symposium on Mathematical Problems in Theoretical Physics, edited by, H. Araki, (Springer-Verlag, Berlin, 1975), Vol. 39.
11. For reviews of the Kuramoto model, see J. A. Acebron, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.77.137 77, 137 (2005); S. H. Strogatz, Physica D 143, 1 (2000); E. Ott, Chaos in Dynamical Systems, 2nd ed. (Cambridge University Press, Cambridge, 2002), Chap., Sec. 6.
12. E. L. Hahn, Phys. Rev. 80, 580 (1950).
13. R. W. Gould, Phys. Lett. 0031-9163 10.1016/0031-9163(65)90110-1 19, 477 (1965); F. W. Crawford and R. S. Harp, J. Appl. Phys. 37, 4405 (1966).
14. E. Ott, J. Plasma Phys. 4, 471 (1970).
15. M. Porkolab and J. Sinnis, Phys. Rev. Lett. 21, 1227 (1968).
16. T. M. O'Neil and R. W. Gould, Phys. Fluids 0031-9171 10.1063/1.1691746 11, 134 (1968); J. H. Malmberg, C. B. Wharton, R. W. Gould, and T. M. O'Neil, Phys. Fluids 11, 1147 (1968).
17. S. H. Strogatz, R. E. Mirollo, and P. C. Matthews, Phys. Rev. Lett. 68, 2730 (1992).
18. T. H. Jensen, J. H. Malmberg, and T. M. O'Neil, Phys. Fluids 0031-9171 10.1063/1.1692734 12, 1728 (1969); C. H. Su and C. Oberman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.20.427 20, 427 (1968); T. M. O'Neil, Phys. Fluids 11, 2420 (1968).
19. E. Ott and T. M. Antonsen, Chaos 18, 037113 (2008).