Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belykh, V.N., N.F. Pederson, O.H. Soerensen, 1977 A: Shunted-Josephson-junction model. I. The autonomous case, Physical Review B 16 (11) (1977) 4853–4859.
Belykh, V.H., N.F. Pederson, O.H. Soerensen, 1977 B: Shunted-Josephson-junction model. II. The nonautonomous case, Physical Review B 16 (11) (1977) 4860–4871.
Cartwright, M.L., J.E. Littlewood: On nonlinear differential equations of the second order: I, J. London Math. Soc. 20 (1945) 180–189.
Chiao, R.Y., M.J. Feldman, M.T. Levinsen, B.A. Tucker: An inverse AC Josephson effect standard, Applied Physics Letters 31 (11) (1977) 776–778.
Crutchfield, J., J.D. Farmer, H. Froehling, N. Packard, R. Shaw: Power spectra and mixing properties of strange attractors, Annals of NY Acad. Science 357 (1979) 453–471.
Crutchfield, J., J.D. Farmer, N. Packard, R. Shaw, G. Jones, R.J. Donelly Power spectral analysis of a dynamical system, Phys. Letters 76A (1980) 1–4.
Crutchfield, J., J.D. Farmer: Fluctuations and simple chaotic dynamics, Preprint.
Crutchfield, J., B.A. Huberman: Fluctuations and the onset of chaos, Phys. Lett. 77A (1980) 407–410.
Crutchfield, J., N. Nauenberg, J. Rudnick: Scaling for external noise at the onset of chaos, Phys. Rev. Lett. 46 (1981) 933–935.
Crutchfield, J., N. Packard: Symbolic dynamics of one dimensional maps, Preprint.
Crutchfield, J.P., B.A. Huberman, N.H. Packard: Noise phenomena in Josephson junctions, App, Phys.Lett. 37 (1980) 750–751.
Crutchfield, J.P., B.A. Huberman: Chaotic states of anharmonic systems in periodic fields, Physical Review Letters 43 (23) (1979) 1743–1747.
Cushman, R.: The periodically driven Josephson equation, (1980), Notes.
Cushman, R., 1982: Periodic solutions of the autonomous Josephson equation, in this Volume.
Fowler, H.A.: Bifurcations, strange attracors, and the modeling of Josephson devices, (A partical bibliography) (1982), National Bureau of Standards, Washington, D.C.
Froehling, H., J.P. Crutchfield, J.D. Farmer, N. Packard: On determining the dimension of chaotic flows, Physica D (1981).
Fulton, T.A.: Externally shunted Josephson junctions, Physical Review B 7 (3) (1973) 1189–1193.
Gallop, J.C.: The impact of superconduction devices, Metrologia 18 (2) (1982) 67–92 (esp. p. 86)
Grasman, J., H. Nijmeyer, E.J.M. Veling: Singular perturbations and mapping on an interval for the forced van der Pol relaxation oscillator (1982) Preprint TW 221, MC.
Grasman, J.: Asymptotic methods for relaxation oscillations, Proc 3rd Scheveningen Conf. on Diff. Equations, North Holland, Math. Studies 31 (1979) 93–111.
Grasman, J.: 1980 A: On the van der Pol oscillator with sinusoidal forcing term, Report TW 207, MC
Grasman, J., 1980 B: Relaxation oscillations of a van der Pol equation with large critical forcing term, Quarterly of Applied Mathematics (1980) 9–16.
Grasman, J.: Dips and slidings of the forced van der Pol relaxation oscillator, (1981) Report TW 214, MC
Henry, R.W., L.D. Jackel, D.E. Prober, S.E.G. Slusky: Simulation of I-V curves of small Josephson tunnel junctions with finite capacitance Preprint.
Henry, R.W., D.E. Prober: Electronic analogs of double-junction and single-junction SQUIDs (1981) Preprint.
Hoppensteadt, F.C., M. Levi, W.L. Miranker: Dynamics of the Josephson junction, Quarterly of Applied Mathematics, 36 (2) (1978) 167–198.
Huberman, B.A., A.B. Zisook: Power spectra of strange attractors, Phys. Rev. Letters 46 (10) (1981) 626–628.
Kaminaga, M.: Solutions of nonlinear equation of a resistively shunted model of Josephson junctions, Journal of the Physical Society of Japan 43 (4) (1977) 1163–1168.
Kamper, R.A., J.E. Zimmerman: Noise thermometry with the Josephson effect, J. Appl. Phys. 42 (1971) 132–136.
Kamper, R.A.: Review of superconduction electronics, IEEE Transactions on Magnetics MAG-11 (2) (1975) 141–146.
Kautz, R.L., G. Costabile: A Josephson voltage standard using a series array of 100 junctions, IEEE Transactions on Magnetics MAG-17 (1) (1981) 780–783.
Kautz R.L.: Chaotic states of rf-biased Josephson junctions, Preprint National Bureau of Standards, Boulder, Colorado (1982).
Kautz, R.L.: On a proposed Josephson-effect voltage standard at zero current bias, Appl. Phys. Lett. 36 (5) (1980) 386–388.
Kautz, R.L.: The ac Josephson effect in hysteretic junctions: range and stability of phase lock, J. Appl. Phys. 52 (5) (1981) 3528–3541.
Landman, B.S.: Calculation of threshold curves for Josephson quantum interference devices, IEEE Transactions on Magnetics MAG-13 (1) (1977) 871–874.
Littlewood, J.E., 1957 A: On non-linear differential equation of second order: III, Acta Math. 97 (1957) 267–308.
Littlewood, J.C., 1957 B: On non-linear differential equation of second order: IV, Acta Math. 98 (1957) 1–110.
Littlewood, J.E.: Some problems in real and complex analysis, Heath, Lexington, Mass. (1968).
McCumber, D.E.: Effect of AC impedance on DC voltage-current characteristics of superconductor weak-link junctions, Journal of Applied Physics 39 (1968) 3113–3118.
Mishchenko, E.F., N.Kh. Rozov: Differential Equations with Small Parameters and Relation Oscillations, Plenum Press, New York (1980), Original: Moscow, 1975.
Packard, N., J.P. Cruchfield, J.D. Farmer, R. Shaw: Geometry from a time series, Phys. Rev. Letters 45 (1980) 712–716.
Parmentier, R.D.: Fluxons in long Josephson junctions, in: Solitions in Action, ed. K. Lonngren & A. Scott, Academic Press, New York (1978) 173–199.
Pederson, N.F., A. Davidson: Chaos and noise rise in Josephson junctions, Appl. Phys. Lett. 39 (10) (1981) 830–832.
Peterson, R.L., R.J. Soulen, D. Van Vechten: Behaviour of the DC impedance of an RF-biaced resistive SQUID, SQUID ’80, ed. H.D. Hahlbohm & H. Lubbig, De Gruyter, Berlin (1980) 569–584.
Peterson, R.L., D. van Vechten: Modeling the impedance of a Josephson-junction noise thermometer, Phys. Rev. B24 (6) (1981) 3588–3591.
Peterson, R.L., D. van Vechten: Modeling the impedance of a resistive RF SQUID, Preprint.
Peterson, R.L.: Mathematical modeling of the impedance of a resistive RF SQUID, J. Appl. Phys. 52 (12) (1981) 7321–7326.
Pontrjagin, L.S.: Uber Autoschwingungssysteme, die den Hamiltonschen nahe liegen, Physikalische Zeitschrift der Sowjetunion 6 (1934) 25–28.
Sanders, J.A., 1982 A: Melnikov’s method and averaging, Celestial Mechanics, 28 (1982) 171–181.
Sanders, J.A., 1982 B: Approach of the boundary layer in the driven Josephson equation, Proceedings of Equadiff ’82, Lecture Notes in Mathematics, Springer-Verlag (1982). to appear.
Sanders, J.A., 1982 C: Report on the driven Josephson equation, Proceedings VII Sitges, Lecture Notes in Physics, Springer-Verlag (1982), to appear.
Sanders, J.A., F. Verhulst: Two chapters in the theory of averaging, (1981) preprint nr. 201, R.U. Utrecht, to appear in a forthcoming monograph.
Schlup, W.A.: I-V characteristics and stationary dynamics of a Josephson junction including the interference term in the current phase relation, J. Phys. C: Solid State Phys. 7 (1974) 736–748.
Schlup, W.A.: Relaxation oscillations of a Josephson contact, ZAMP, 30 (1979) 851–857.
Shaw, R.: Strange attractors, chaotic behaviour, and information flow, Z. Naturforsch. 36a (1981) 80–112.
Soerensen, O.H.: Analysis of the ac SQUID with low inductance and low critical current, Journal of Applied Physics 47 (1976) 5031–5037.
Somervuo, P.: Parametric amplification using a point contact Josephson junction, Acta Polytechnica Scandinavica 40 (1976) 7–34.
Soulen Jr., R.J., R.P. Giffard: Impedance and noise of an rf-biased RSQUID operated in the non-hysteretic regime, Appl. Phys. Lett. 32 (1978) 770.
Soulen Jr., R.J., H. Seppa, D. van Vechten: The effect of additive noise & bandpass filters on the performance of a Josephson junction (1982), National Bureau of Standards, Washington, D.C.
Stewart, W.C.: Current-voltage characteristics of Josephson junctions, Appl. Phys. Letters 12 (8) (1968) 277–280.
Sugrobov, G.V.: Approximate representation of relaxation oscillations. Differential Equations 12 (1976) 256–258.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Sanders, J.A. (1983). The (Driven) Josephson equation: An exercise in asymptotics. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062372
Download citation
DOI: https://doi.org/10.1007/BFb0062372
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12286-9
Online ISBN: 978-3-540-39612-3
eBook Packages: Springer Book Archive