Stability of Periodic Solutions in Series Arrays of Josephson Junctions with Internal Capacitance

Journal of Nonlinear Science

Volumn 7, Issue 6, 1997, Pages 503-536

  Watanabe, S ^a   Swift, J W ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b NORTHERN ARIZONA UNIVERSITY   (United States)

Author keywords

Bifurcation; Breakdown of global foliation; Josephson junction arrays; Multiple time scale analysis; Nonlinear oscillations; Stability of periodic solutions

Indexed keywords

EID: 0000984323     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329900038     Document Type: Article

References (38)

1. D.G. Aronson, M. Krupa, and P. Ashwin, "Semirotors in the Josephson junction equations," preprint (1995).
2. D.G. Aronson and YS. Huang, "Single wave-form solutions for general arrays of Josephson junctions," preprint (1995).
3. 1994 Applied Superconductivity Conference Proceedings, IEEE Trans. Appl. Supercond. 5, no. 2, pt. 1 (1995).
4. P. Ashwin and J.W. Swift, "The dynamics of n identical oscillators with symmetric coupling," J. Nonlin. Sci. 2, 69-108 (1992).
5. P. Ashwin and J.W. Swift, "Unfolding the torus: Oscillator geometry from time delays," J. Nonlin. Sci. 3, 459-475 (1993).
6. S.P. Benz and C.J. Burroughs, "Two-dimensional arrays of Josephson junctions as voltage-tunable oscillators," Supercond. Sci. Tech. 4, 561-567 (1991).
7. Y. Braiman and K. Wiesenfeld, "Global stabilization of a Josephson-junction array," Phys. Rev. B 49, no. 21, 15223-15226 (1994).
8. A.A. Chernikov and G. Schmidt, "Conditions for synchronization in Josephson-junction arrays," Phys. Rev. E 52, no. 4, pt. A, 3415-3419 (1995).
9. M. Darula, P. Seidel, and A. Darulova, "Coherent states in a multi-junction superconducting loop," Europhys. Lett. 33, no. 1, 41-46 (1996).
10. E.J. Doedel and J.P. Kernévez, "Auto: Software for continuation and bifurcation problems in ordinary differential equations," Technical Report, California Institute of Technology, Applied Mathematics (1986).
11. P. Hadley and M.R. Beasley, "Dynamical states and stability of linear arrays of Josephson junctions," J. Appl. Phys. 50, no. 10, 621-623 (1987).
12. P. Hadley, M.R. Beasley, and K. Wiesenfeld, "Phase locking of Josephson-junction series arrays," Phys. Rev. B 38, no. 13, 8712-8719 (1988).
13. V. Hakim and W.-J. Rappel, "Dynamics of the globally coupled complex Ginzburg-Landau equation," Phys. Rev. A 46, no. 12, R7347-7350 (1992).
14. E. B. Harris and J. C. Garland, "Voltage splay modes in a modified linear Josephson array," preprint (1996).
15. A.K. Jain, K.K. Likharev, J.E. Lukens and J.E. Sauvageau, "Mutual phase-locking in Josephson junction arrays," Phys. Rep. 109, 310-426 (1984).
16. Technical review of Josephson junctions and arrays can be found in Physica B 152, 1-302 (1988), as well as in [ASC94].
17. K. Kaneko, "Globally coupled circle maps," Physica 54D, 5-19 (1991).
18. R.L. Kautz, C. A. Hamilton, and F. L. Lloyd, "Series-array Josephson voltage standards," IEEE Trans. Mag. 23, 883-890 (1987).
19. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, Berlin (1984).
20. M. Levi, F.C. Hoppensteadt, and W.L. Miranker, "Dynamics of the Josephson junction," Quart. Appl. Math., 167-198 (July 1978).
21. K. K. Likharev, Dynamics of Josephson Junctions and Circuits, Gordon and Breach, New York (1986).
22. H.-G. Meyer and W. Krech, "Phase-locking in series arrays of Josephson junctions shunted by a complex load," J. Appl. Phys. 68, 2868-2874 (1990).
23. N. Nakagawa and Y. Kuramoto, "From collective oscillations to collective chaos in a globally coupled oscillator system," Physica 75D, 74-80 (1994).
24. S. Nichols and K. Wiesenfeld, "Ubiquitous neutral stability of splay-phase states." Phys. Rev. A 45, no. 12, 8430-8435 (1992).
25. K. Otsuka, "Winner-takes-all dynamics and antiphase states in modulated multi-mode lasers," Phys. Rev. Lett. 67, no. 9, 1090-1093 (1991).
26. W.-J. Rappel, "Dynamics of a globally-coupled laser model." Phys. Rev. E 49, no. 4, pt. A. 2750-2755 (1994).
27. I.B. Schwartz and K.Y. Tsang. "Antiphase switching in Josephson junction arrays," Phys. Rev. Lett. 73, no. 21, 2797-2800 (1994).
28. M. Silber, L. Fabiny, and K. Wiesenfeld, "Stability result for in-phase and splay-phase states of solid-state laser arrays," J. Opt. Soc. Am. B 10, no. 6, 1121-1129 (1993).
29. S.H. Strogatz and R.E. Mirollo, "Stability of incoherence in a population of coupled oscillators," J. Stat. Phys. 63, no. 3/4, 613-635 (1991).
30. S.H. Strogatz and R.E. Mirollo, "Splay states in globally coupled Josephson arrays: Analytical prediction of Floquet multipliers," Phys. Rev. E 47, no. 1, 220-227 (1993).
31. J.W. Swift, S.H. Strogatz, and K. Wiesenfeld, "Averaging of globally coupled oscillators," Physica D 55, 239-250 (1992).
32. E. Terzioglu and M.R. Beasley, "Series Josephson junction arrays as a high output voltage amplifier," IEEE Trans. Appl. Supercond. 5, no. 2, pt. 3, 3349-3352 (1995).
33. K.Y. Tsang, R.E. Mirollo, S.H. Strogatz, and K. Wiesenfeld, "Dynamics of a globally coupled oscillator array," Physica D 48, 102-112 (1991).
34. K.Y. Tsang and I.B. Schwartz, "Interhyperhedral diffusion in Josephson-junction arrays," Phys. Rev. Lett. 68, no. 15, 2265-2268 (1992).
35. H.S.J. van der Zant, T.P. Orlando, S. Watanabe, and S.H. Strogatz, "Vortices trapped in discrete Josephson rings," Physica B 203, 490-496 (1994).
36. S. Watanabe and S.H. Strogatz, "Constants of motion for superconducting Josephson arrays," Physica D 74, 197-253 (1994).
37. S. Watanabe, S.H. Strogatz, H.S.J. van der Zant, T.P. Orlando, "Whirling modes and parametric instabilities in the discrete sine-Gordon equation: Experimental tests in Josephson rings," Phys. Rev. Lett. 74, no. 3, 379-382 (1995).
38. K. Wiesenfeld and J.W. Swift, "Averaged equations for Josephson junction series arrays," Phys. Rev. E 51, 1020-1025 (1995).