Bifurcations of periodic solutions and chaos in Josephson system

Discrete and Continuous Dynamical Systems

Volumn 7, Issue 3, 2001, Pages 573-592

  Jing, Zhujun ^a,b   Chan, K Y ^c   Xu, Dashun ^b   Cao, Hongjun ^b  

^a HUNAN NORMAL UNIVERSITY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bifurcations; Chaos; Josephson systems; Periodic solution; Second order averaging and Melnikov methods

Indexed keywords

EID: 0035609099     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2001.7.573     Document Type: Article

References (35)

1. Belyky, V.N., Pedersen, N.F. and Soerensen, O.H., Shunted-Josephson model, I. The autonomous, II. The non-autonomous case, Phys. Rev. B., 16 (1977), 4853-4871.
2. Ben-Jacobi, E., Goldhirsch, I., Imry, Y. and Fishman, S., Intermittent chaos in Josephson junctions, Phys. Rev. Lett., 49 (1982), 1599-1602.
3. Chua, L.O. and Tang, Y.S., Nonlinear oscillation via voltage series, IEEE Trans, Circuits Syst., AS-2913 (1982), 150-168.
4. Chua, L.O., Desoe, C.A. and Kuch, E.S., "Linear and Nonlinear Circuits", McGraw-hill, New York, 1987.
5. Cirillo, M. and Perdersen, N.F., On Bifurcation and transition to chaos in a Josephson junction, Phys. Letter, 90 A(3) (1982), 150-152.
6. Cushman, R., Periodic solutions of the autonomous Josephson equation, in "Lecture Notes in Math.", vol. 985, (1983), 319-326.
7. Davidson, A., Dueholm, B. and Beasley, M.R., Experiments on intrinsic and they may included chaos in an RF-driven Josephson junction, Phys. Rev. B., 33 (1986), 5127-5136.
8. D'Humieres, D., Beasley, M.R., Huberman, B.A, and Libchaber, A.F., Chaotic states and routes to chaos in the forced pendulum, Phys. Rev. A., 26(6) (1982), 3483-3492.
9. Graham, R. and Keymer, J., Level repulsion in power spectra of chaotic Josephsonjunctions, Phys. Rev. A., A(44) (1991), 6281-6291.
10. Graham, R., Schlantman, M. and Keymer, J., Dynamical localization in Josephson junctions, Phys. Rev. Lett., 67 (1991), 255-272.
11. Levi, M., Hoppensteadt, F. and Miranker, W., Dynamics of the Josephson junction, Quart, Appl. Math., 35 (1978), 167-198.
12. Li, G.X. and Moon, F.C., Criteria for chaos of a three-well potential oscillator with homoclinic and heteroclinic orbits, J. Sound and Vibrations, 136(1) (1990), 17-34.
13. Guckenheimer, J. and Holmes, P., "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields," Springer-Verlag, New York, 1983.
14. Lindsey, W.C., "Synchronization Systems In Communication And Control," Prentice-Hall, New Jersey, 1972.
15. Levinsen, M.T., The chaotic oscilloscope, Amer. J. Phys., 61 (1993), 155-193.
16. Jing, Zhu-Jun, Application of qualitative methods of differential equations to study phase-locked loops, SIAM J. Appl. Math., 43(6)(1983), 1749-1758.
17. Jing, zhu-Jun, Chaotic behavior in the Josephson equations with periodic force, SIAM J. Appl. Math., 49(6) (1989), 847-856.
18. Josephson, D., Phys. Lett., 1(1962), 251; Adv. Phys., 14 (1965), 419.
19. Josephson, D., Phys. Lett., 1(1962), 251; Adv. Phys., 14 (1965), 419.
20. Kapitaniak, Thomas, "Chaotic Oscillators Theory and Applications," World Scientific, Singapore, 1992.
21. Korsch, H.J. and Jodj, H.J., "Chaos-A Program Collection for the PC," Springer-Verlag, 1994.
22. Moon, F.C., "Chaotic Vibrations: A Introduction For Applied Scientists And Engineers," John Wiley, 1987.
23. Pai, M.A., Sauer, P.W., Lesieutre, B.C. and Adapa, R., Structural stability in power systems-effect of load models, IEEE Trans. on Power Systems, 10(02) (1995), 609-615.
24. Rasband, S.N., "Chaotic Dynamics of Nonlinear Systems," Wiley, New York, 1990.
25. Sanders, J.A. and Verhulst, F., "Averaging Methods in Nonlinear Dynamical Systems", Applied Mathematics Sciences, vol. 59, Springer-Verlag, New York, 1985.
26. Salam, F.M.A. and Satry, S., Dynamics of the forced Josephson junction circuit: the regions of chaos, IEEE Trans. Circuits and Systems, 32 (1985), 784-796.
27. Sanders, J.A. and Cushman, R.H., Limit cycles in Josephson equation, SIAM. J. Math. Anal., 17 (1986), 495-511.
28. Sanders, J.A., The (Driven) Josephson equations: An exercise in asymptotics, in Lecture Notes in Math., vol. 985, 288-318, (1983).
29. Schecter, S., The saddle-node separatrix-loop bifurcation, SIAM. J. Math. Anal., 18(4) (1987), 1142-1156.
30. Schecter, S., Melnikov's method at a saddle-node and the dynamics of the forced Josephson junction, SIAM. J. Math. Anal., 18(6) (1987), 1699-1715.
31. Szemplinska-Stupnicka, W, Iooss, G. and Moon, F.C., "Chaotic Motions in Nonlinear Dynamicalsystems," Springer-Verlag, 1988.
32. Wiggins, S., "Introduction to Applied Nonlinear Dynamical Systems and Chaos," Springer-Verlag, New York, 1990.
33. Yagasaki, K., A simple feedback control system: Bifurcations of periodic orbits and chaos, Nonlinear Dynamics, 9 (1996), 391-417.
34. Yagasaki, K., Chaos in a pendulum with feedback control, Nonlinear Dynamics, 6 (1994), 125-142.
35. Yeh, W.J. and Kao, Y.H., Intermittence in Josephson junctions, Appl. Phys. Lett., 42 (1983), 299-.