Synchronization of coupled rotators: Josephson junction ladders and the locally coupled Kuramoto model

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

Volumn 67, Issue 2 2, 2003, Pages 262161-2621614

  Daniels, B C ^a   Dissanayake, S T M ^a   Trees, B R ^a  

^a OHIO WESLEYAN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAPACITANCE; ELECTRIC POTENTIAL; OSCILLATORS (ELECTRONIC); SUBMILLIMETER WAVES;

COUPLED ROTATORS;

JOSEPHSON JUNCTION DEVICES;

EID: 0037720199     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. A.T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 1980).
2. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin, 1984).
3. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
4. A.T. Winfree, J. Theor. Biol. 16, 15 (1967).
5. Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, edited by H. Araki, Lecture Notes in Physics, Vol. 39 (Springer, New York, 1975). See also Ref. [2].
6. For a historical and mathematical review of basic aspects of the GKM, see S.H. Strogatz, Physica D 143, 1 (2000).
7. S.H. Strogatz and R.E. Mirollo, Physica D 31, 143 (1988).
8. Z. Liu, Y.-C. Lai, and F.C. Hoppensteadt, Phys. Rev. E 63, 055201 (2001).
9. Z. Zheng, G. Hu, and B. Hu, Phys. Rev. Lett. 81, 5318 (1998).
10. S. Shinomoto and Y. Kuramoto, Prog. Theor. Phys. 75, 1319 (1986).
11. R.S. Newrock, C.J. Lobb, U. Geigenmüller, and M. Octavio, Solid State Physics (Academic Press, San Diego, 2000), Vol. 54.
12. B. Vasilić, P. Barbara, S.V. Shitov, and C.J. Lobb, Phys. Rev. B 65, 180503 (2002).
13. G. Filatrella, B. Straughn, and P. Barbara, J. Appl. Phys. 90, 5675 (2001).
14. M. Darula, T. Doderer, and S. Beuven, Supercond. Sci. Technol. 12, R1 (1999).
15. M.V. Fistul and J.B. Page, Phys. Rev. E 64, 036609 (2001); E. Trías, J.J. Mazo, and T.P. Orlando, Phys. Rev. Lett. 84, 741 (2000); P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, and Y. Zolotaryuk, ibid. 84, 745 (2000).
16. M.V. Fistul and J.B. Page, Phys. Rev. E 64, 036609 (2001); E. Trías, J.J. Mazo, and T.P. Orlando, Phys. Rev. Lett. 84, 741 (2000); P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, and Y. Zolotaryuk, ibid. 84, 745 (2000).
17. M.V. Fistul and J.B. Page, Phys. Rev. E 64, 036609 (2001); E. Trías, J.J. Mazo, and T.P. Orlando, Phys. Rev. Lett. 84, 741 (2000); P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, and Y. Zolotaryuk, ibid. 84, 745 (2000).
18. For example, see B.R. Trees, in Studies of High Temperature Superconductors (NOVA Science Publishers, New York, 2001), Vol. 39.
19. K. Wiesenfeld, P. Colet, and S.H. Strogatz, Phys. Rev. Lett. 76, 404 (1996).
20. K. Wiesenfeld, P. Colet, and S.H. Strogatz, Phys. Rev. E 57, 1563 (1998).
21. H.-A. Tanaka, A.J. Lichtenberg, and S. Oishi, Phys. Rev. Lett. 78, 2104 (1997); Physica D 100, 279 (1997).
22. H.-A. Tanaka, A.J. Lichtenberg, and S. Oishi, Phys. Rev. Lett. 78, 2104 (1997); Physica D 100, 279 (1997).
23. cR product has been found to be quite uniform in arrays of SNS junctions. See S.P. Benz, Appl. Phys. Lett. 67, 2714 (1995).
24. Actually, Eqs. (6) and (7) result in 3N - 1 equations in 3N - 2 unknowns. We therefore do not apply Eq. (6b) to the lower right node (chosen arbitrarily). A similar effect arises in the solution of the RSJ equations for the superconducting phases at the 2N nodes of the array. In that case, one must arbitrarily set the phase at one of the nodes to zero, i.e., ground a node.
25. G. Filatrella and K. Wiesenfeld, J. Appl. Phys. 78, 1878 (1995).
26. See Refs. [17] and [18] as well as: J.W. Swift, S.H. Strogatz, and K. Wiesenfeld, Physica D 55, 239 (1992); K. Wiesenfeld and J.W. Swift, Phys. Rev. E 51, 1020 (1995).
27. See Refs. [17] and [18] as well as: J.W. Swift, S.H. Strogatz, and K. Wiesenfeld, Physica D 55, 239 (1992); K. Wiesenfeld and J.W. Swift, Phys. Rev. E 51, 1020 (1995).
28. See Ref. [7] or also A.H. Cohen, P.J. Holmes, and R.H. Rand, J. Math. Biol. 13, 345 (1982).
29. c when solving the RSJ equations numerically.
30. A. Barone and G. Paternó, Physics and Applications of the Josephson Effect (Wiley, New York, 1982).
31. C.D. Tesche and J. Clarke, J. Low Temp. Phys. 29, 301 (1977).
32. B.J. Kim, M.-S. Choi, P. Minnhagen, G.S. Jeon, H.J. Kim, and M.Y. Choi, Phys. Rev. B 63, 104506 (2001).
33. M. Qian and X.J. Zhang, Phys. Rev. E 65, 031110 (2002).
34. H.-A. Tanaka, A.J. Lichtenberg, and S. Oishi, Phys. Rev. Lett. 78, 2104 (1997).
35. H.-A. Tanaka, A.J. Lichtenberg, and S. Oishi, Physica D 100, 279 (1997).
36. H. Hong and M.Y. Choi, Phys. Rev. E 62, 6462 (2000).