Tutorials and ReviewsNo Access

BIFURCATIONS OF PERIODIC ORBITS IN A JOSEPHSON EQUATION WITH A PHASE SHIFT

Institute of Mathematics, Chinese Academia of Sciences, Beijing 100080, P.R. China

Department of Mathematics, Hunan Normal University, Hunan, Changsha, P.R. China

and

Institute of Mathematics, Chinese Academia of Sciences, Beijing 100080, P.R. China

Current Address:Super Computing Center, Computer Network Information Center, Chinese Academy of Science, P.O. Box 349, Beijing 100080, P. R. China.

Search for more papers by this author

https://doi.org/10.1142/S0218127402005261Cited by:12 (Source: Crossref)

Abstract

The Josephson equation with constant current and sinusoidal forcings and a phase shift is investigated in detail: the existence and the bifurcations of harmonics and subharmonics under small perturbations are given, by using the second-order averaging method and Melnikov function; the influence on bifurcations of periodic or subharmonics as the phase shift varies is considered; some numerical simulation results are reported in order to prove our theoretical predictions.

Keywords:

References

A. A. Abidi and L. O. Chua, Electron. Circuits Syst. 3, 186 (1979). Web of Science, Google Scholar
M. Bartuccelliet al., Phys. Rev. B 33, 4686 (1986). Web of Science, Google Scholar
V. N. Belyky, N. F. Pedersen and O. H. Soerensen, Phys. Rev. B 16, 4853 (1977). Web of Science, Google Scholar
H. J. Cao and Z. J. Jing, Chaos Solit. Fract. 14, 1887 (2001). Google Scholar
D. D'Humiereset al., Phys. Rev. 26, 3483 (1982). Web of Science, Google Scholar
J. Guckenheimer and P. Holmes , Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ( Springer-Verlag , NY , 1983 ) . Google Scholar
C. Holmes and P. Holmes, J. Sound Vib. 78, 161 (1981). Web of Science, Google Scholar
Z. J. Jing, SIAM J. Appl. Math. 43, 1749 (1983). Google Scholar
Z. J. Jing, SIAM J. Appl. Math. 49, 847 (1989). Google Scholar
Z. J. Jinget al., Discrete and Continuous Dynamical Systems – Series A 7, 573 (2001). Web of Science, Google Scholar
D. Josephson, Phys. Lett. 1, 251 (1962). Web of Science, Google Scholar
D. N. Landberg and D. J. Scalapion, Sci. Am. 21, 30 (1966). Google Scholar
M. Levi, F. Hoppenstesdt and W. Miranker, Quart. Appl. Math. 35, 167 (1978). Google Scholar
J. Matisoo, IEEE Trans. Magn. 5, 848 (1969). Web of Science, Google Scholar
V. K. Melnikov, Trans. Moscow Math. Soc. 12, 1 (1963). Google Scholar
M. Odyniec and L. O. Chua, IEEE Trans. Circuits Syst. CAS-32, 34 (1985). Google Scholar
S. N. Rasband , Chaotic Dynamics of Nonlinear System ( Wiley , NY , 1990 ) . Google Scholar
J. A. Sanders and F. Verhulst , Averaging Methods in Nonlinear Dynamical Systems , Applied Mathematics Sciences 59 ( Springer-Verlag , NY , 1985 ) . Google Scholar
J. A. Sanders and R. H. Cushman, SIAM J. Math. Anal. 17, 495 (1986). Web of Science, Google Scholar
S. Schecter, SIAM J. Math. Anal. 18, 1699 (1987). Web of Science, Google Scholar
W. A. Schlup, J. Phys. C. Solid State Phys. 7, 736 (1974). Web of Science, Google Scholar
S. Wiggins , Introduction to Applied Nonlinear Dynamical Systems and Chaos ( Springer-Verlag , NY , 1990 ) . Google Scholar
K. Yagasaki, J. Sound Vib. 190, 587 (1996). Web of Science, Google Scholar