Collective phase slips and phase synchronizations in coupled oscillator systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 1 A, 2000, Pages 402-408

  Zheng, Zhigang ^a,b   Hu, Bambi ^b,c   Hu, Gang ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^c University of Houston   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; HEURISTIC METHODS; NATURAL FREQUENCIES; RANDOM PROCESSES; SET THEORY;

COUPLED OSCILLATOR SYSTEMS; GAUSSIAN DISTRIBUTION; GLOBAL PHASE LOCKING; HETEROCLINIC PATH INSTABILITY; LOCAL CLUSTERING; PHASE SLIPS; PHASE SYNCHRONIZATIONS; QUASIPERIODICITY;

OSCILLATIONS;

EID: 0034227904     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.402     Document Type: Article

References (31)

1. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
2. A. T. Winfree, Geometry of Biological Time (Springer-Verlag, New York, 1990).
3. H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983).
4. T. D. Clark, Phys. Lett. 27A, 585 (1968); R. Bonifacio et al., ibid. 101A, 427 (1984); D. R. Tilley, ibid. 33A, 205 (1970); K. Wiesenfeld et al., Phys. Rev. Lett. 76, 404 (1996).
5. T. D. Clark, Phys. Lett. 27A, 585 (1968); R. Bonifacio et al., ibid. 101A, 427 (1984); D. R. Tilley, ibid. 33A, 205 (1970); K. Wiesenfeld et al., Phys. Rev. Lett. 76, 404 (1996).
6. T. D. Clark, Phys. Lett. 27A, 585 (1968); R. Bonifacio et al., ibid. 101A, 427 (1984); D. R. Tilley, ibid. 33A, 205 (1970); K. Wiesenfeld et al., Phys. Rev. Lett. 76, 404 (1996).
7. T. D. Clark, Phys. Lett. 27A, 585 (1968); R. Bonifacio et al., ibid. 101A, 427 (1984); D. R. Tilley, ibid. 33A, 205 (1970); K. Wiesenfeld et al., Phys. Rev. Lett. 76, 404 (1996).
8. F. Ritort, Phys. Rev. Lett. 80, 6 (1998).
9. S. Ichimaru, Basic Principles of Plasma Physics: A Statistical Approach (Addison-Wesley, Reading, MA, 1980).
10. A. H. Cohen, P. J. Holmes, and R. H. Rand, J. Math. Biol. 13, 345 (1982).
11. N. Kopell and G. B. Ermentrout, Commun. Pure Appl. Math. 39, 623 (1986).
12. S. H. Strogatz and R. E. Mirollo, J. Phys. A 21, L699 (1988); Physica D 31, 143 (1988).
13. S. H. Strogatz and R. E. Mirollo, J. Phys. A 21, L699 (1988); Physica D 31, 143 (1988).
14. L. Glass and M. C. Mackey, From Clocks to Chaos, The Rhythm of Life (Princeton Univ. Press, Princeton, NJ, 1988).
15. C. Schafer et al., Nature (London) 392, 239 (1998).
16. P. Tass et al., Phys. Rev. Lett. 81, 3291 (1998).
17. J. Buck and E. Buck, Sci. Am. 234, 74 (1976); J. Buck, Q. Rev. Biol. 63, 265 (1988).
18. J. Buck and E. Buck, Sci. Am. 234, 74 (1976); J. Buck, Q. Rev. Biol. 63, 265 (1988).
19. T. J. Walker, Science 166, 891 (1969).
20. R. D. Traub, R. Miles, and R. K. S. Wong, Science 243, 1319 (1989).
21. M. K. McClintock, Nature (London) 229, 244 (1971).
22. T. Yalcmkaya and Y. C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
23. M. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996); G. V. Osipov, A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Phys. Rev. E 55, 2353 (1997).
24. M. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996); G. V. Osipov, A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Phys. Rev. E 55, 2353 (1997).
25. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
26. E. Rosa, Jr., E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998); K. J. Lee, Y. Kwak, and T. K. Lim, ibid. 81, 321 (1998).
27. E. Rosa, Jr., E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998); K. J. Lee, Y. Kwak, and T. K. Lim, ibid. 81, 321 (1998).
28. Z. Zheng, G. Hu, and B. Hu, Phys. Rev. Lett. 81, 5318 (1998).
29. u = π, and heteroclinic orbits linking Δθ= (2m - 1 ) π and Δθ= (2m + 1) π, m = . . . , - 2, - 1,0,1,2, . . . , appear at the bifurcation point K = 3|ω|/2. This picture can be extended to the case of Eq. (1), though the latter case is more complicated and it is impossible to compute the explicit form of the heteroclinic orbits.
30. Y. Pomeau and P. Maneville, Commun. Math. Phys. 74, 189 (1980).
31. G. Hugenii, Horoloquim Oscilatorium (Parisüs, Paris, 1673).