Resonant regions of Josephson junction equation in case of large damping. (English) Zbl 1220.81181
Summary: The dynamics of Josephson junction equation in case of damping \(\alpha >2\) is investigated numerically. In this case the second-order system can be asymptotically reduced in the large to a one-dimensional circle map. We study the parametric dependence of the resonances of this system and plot the resonant regions in two-dimensional parameter space. The periodic variation of the widths of harmonic regions with increase of the periodic driving force is observed. In the limit of infinite damping, we study a first order system through suitable re-scaling and the same property is observed. We conjecture this may caused by the competition between the periodic potential and the periodic external driving in these systems.
MSC:
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 82D55 | Statistical mechanics of superconductors |
| 55M25 | Degree, winding number |
| 82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
| 37L10 | Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems |
| 70K28 | Parametric resonances for nonlinear problems in mechanics |
References:
| [1] | Belykh, V. N.; Pedersen, N. F.; Sorensen, O. H., Phys. Rev. B, 16, 4853 (1977) |
| [2] | Huberman, B. A.; Crutchfield, J. P.; Packark, N. H., Appl. Phys. Lett., 37, 750 (1980) |
| [3] | Kautz, R. L.; Monaco, R., J. Appl. Phys., 57, 875 (1985) |
| [4] | Wiesenfeld, K.; Knobloch, E.; Miracky, R. F.; Clarke, J., Phys. Rev. A, 29, 2101 (1984) |
| [5] | Wenxian, S., Acta Math. Appl. Sin., 5, 242 (1989) |
| [6] | Braun, O. M.; Kivshar, Y. S., The Frenkel-Kontorova Model: Concepts, Methods, and Applications (2003), Springer |
| [7] | Jung, P.; Kissner, J. G.; Hänggi, P., Phys. Rev. Lett., 76, 3436 (1996) |
| [8] | Zapata, I.; Łuczka, J.; Sols, F.; Hänggi, P., Phys. Rev. Lett., 80, 829 (1998) |
| [9] | Trías, E.; Mazo, J. J.; Falo, F.; Orlando, T. P., Phys. Rev. E, 61, 2257 (2000) |
| [10] | Goldobin, E.; Sterck, A.; Koelle, D., Phys. Rev. E, 63, 031111 (2001) |
| [11] | Barbara, P.; Lawthorne, A. B.; Shitov, S. V.; Lobb, C. J., Phys. Rev. Lett., 82, 1963 (1999) |
| [12] | Qin, W.-x.; Chen, G., Physica D, 197, 375 (2004) · Zbl 1066.34046 |
| [13] | Min, Q.; Xian, S. W.; Jinyan, Z., J. Differential Equations, 71, 315 (1988) · Zbl 0652.34054 |
| [14] | Levi, M., Phys. Rev. A, 37, 927 (1988) |
| [15] | Rasmussen, K.; Zharnitsky, V.; Mitkov, I.; Gronbech-Jensen, N., Phys. Rev. B, 59, 58 (1999) |
| [16] | Chen, L.; Chen, P.; Ong, C. K., Appl. Phys. Lett., 80, 1025 (2002) |
| [17] | Glass, L.; Perez, R., Phys. Rev. Lett., 48, 1772 (1982) |
| [18] | Zhang, X.-J., J. Phys. A, 34, 10859 (2001) |
| [19] | Jensen, M. H.; Bak, P.; Bohr, T., Phys. Rev. A, 30, 1960 (1984) |
| [20] | Pikovsky, A.; Rosenblum, M.; Kurths, J., Synchronization: A Universal Concept in Nonlinear, Science (2001), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0993.37002 |
| [21] | Adler, R., Proc. IEEE, 61, 1380 (1973) |
| [22] | Barone, A.; Paterno, G., Physics and Applications of the Josephson Effect (1982), John Wiley & Sons |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
