Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-19T11:26:01.316Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochasticity in the Josephson map

Published online by Cambridge University Press:  13 March 2009

Y. Nomura ,
Y. H. Ichikawa  and
A. T. Filipov
Y. Nomura
Affiliation:
Fukui National College of Technology, Sabae 916, Japan
Y. H. Ichikawa
Affiliation:
College of Engineering, Chubu University, Kasugai 487, Japan
A. T. Filipov
Affiliation:
Joint institute for Nuclear Research, Dubna 141980, Russian Federation
Get access Rights & Permissions [Opens in a new window]

Abstract

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 493 - 506
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Filipov, A. T. and Gal'pern, Yu. S. 1983 Bifurcations of soliton bound states in nonuniform Josephson junctions. Solid State Commun. 48, 665–669.CrossRefGoogle Scholar
Filipov, A. T. and Gal'pern, Yu. S. 1993 Bound states, bifurcations and static chaos in Josephson lattices. Phys. Lett. 172A, 471–477.CrossRefGoogle Scholar
Filipov, A. T., Gal'pern, Yu. S., Boyadjiev, T. L. and Puzynin, I. V. 1987 Critical currents in Josephson junctions with micro inhomogeneities attracting solitons. Phys. Lett. 120A, 47–50.CrossRefGoogle Scholar
Fulton, T. A., Dynes, R. C. and Anderson, P. W. 1973 The flux shuttle - a Josephson junction shift register employing single flux quanta. Proc. IEEE 61, 28–33.CrossRefGoogle Scholar
Gal'pern, Yu. S. and Filipov, A. T. 1982 Soliton bound states in long Josephson junction. JETP Lett. 35, 580–587.Google Scholar
Gal'pern, Yu. S., Filipov, A. T. 1984 Bound states of solitons in inhomogeneous Josephson junctions. Soviet Phys. JETP 59, 894–903.Google Scholar
Green, J. M. 1979 A method for determining a stochastic transition. J. Math. Phys. 20, 1183–1201.CrossRefGoogle Scholar
Ichikawa, Y. H., Kamimura, T. and Hatori, T. 1987 Stochastic diffusion in the standard map. Physica D29, 247–255.Google Scholar
Ichikawa, Y. H., Kamimura, T., Hatori, T. and Kim, S. Y. 1989 Stochasticity and symmetry of the standard map. Prog. Theor. Phys. Suppl. 98, 1–18.CrossRefGoogle Scholar
McLaughlin, D. C. and Scott, A. C 1978 Perturbation analysis of fluxon dynamics. Phys. Rev. A18, 1652–1680.CrossRefGoogle Scholar
Vystavkin, A. N., Drachevsky, Yu. F., Koshelets, V. P. and Serpuchenko, I. L. 1988 First observation of static bound states of fluxons in long Josephson junction with inhomogeneites. Fiz. Niz. Temp. 14, 646–649.Google Scholar
See also Proceedings of the International Superconductor Electronics Conference, ISEC-89, Tokyo, 1989.Google Scholar