Dynamical Analysis and Microcontroller Implementation of Linear Resistor-Capacitor Shunted Josephson Junction Model

Year 2021, Volume: 3 Issue: 2, 55 - 58, 30.11.2021

Tokoue Ngatcha Dianorré Abba Oum Alhadji Alex Stéphane Kemnang Tsafack , Sifeu T. Kingni

https://doi.org/10.51537/chaos.946929

Cited By: 11

Abstract

Theoretical analysis and microcontroller implementation of linear resistive-capacitive shunted Josephson junction (LRCSJJ) model are investigated in this paper. The rate-equations describing the LRCSJJ model has two or no equilibrium points relying on the external direct current (DC). One of the equilibrium points is a stable node and the other one is a saddle node. The hysteresis loop of current-voltage characteristics increases with the increasing of the capacitance of Josephson junction (JJ). Excitable mode, limit cycle, periodic and chaotic behaviors are found in LRCSJJ model with external alternative current thanks to the two modulation parameters largest Lyapunov exponents (LLE) diagram. LRCSJJ model exhibits two different shapes of chaotic attractors by varying the modulation amplitude. Finally, the existence of chaotic behaviors is confirmed by microcontroller results obtained from the microcontroller implementation of LRCSJJ model.

Keywords

Chaos, Josephson junction, hysteresis loop, excitable mode, Microcontroller implementation

References

• Bartuccelli, M., P. L. Christiansen, N. F. Pedersen, and M. P. Sørensen, 1986 Prediction of chaos in a josephson junction by the melnikov-function technique. Physical Review B 33: 4686.
• Cawthorne, A., C. Whan, and C. Lobb, 1998 Complex dynamics of resistively and inductively shunted josephson junctions. Journal of applied physics 84: 1126–1132.
• Dana, S. K., D. C. Sengupta, and K. D. Edoh, 2001 Chaotic dynamics in josephson junction. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48: 990–996.
• Dana, S. K., D. C. Sengupta, and C.-K. Hu, 2006 Spiking and bursting in josephson junction. IEEE Transactions on Circuits and Systems II: Express Briefs 53: 1031–1034.
• Kautz, R. L. and R. Monaco, 1985 Survey of chaos in the rf-biased josephson junction. Journal of applied physics 57: 875–889.
• Levi, M., F. C. Hoppensteadt, and W. Miranker, 1978 Dynamics of the josephson junction. Quarterly of Applied Mathematics 36: 167–198.
• Likharev, K., 1986 Dynamics of josephson junctions and circuits gordon and breach. New York p. 92.
• Malishevskii, A. and S. Uryupin, 2020 Current-voltage characteristics of radiating josephson sandwich. Physics Letters A 384: 126515.
• McCumber, D., 1968 Effect of ac impedance on dc voltage-current characteristics of superconductor weak-link junctions. Journal of Applied Physics 39: 3113–3118.
• Neumann, E. and A. Pikovsky, 2003 Slow-fast dynamics in josephson junctions. The European Physical Journal B-Condensed Matter and Complex Systems 34: 293–303.
• Ojo, K., A. Adelakun, and A. Oluyinka, 2019 Synchronisation of cyclic coupled josephson junctions and its microcontroller-based implementation. Pramana 92: 1–7.
• Salam, F. and S. Sastry, 1985 Dynamics of the forced josephson junction circuit: the regions of chaos. IEEE transactions on circuits and systems 32: 784–796.
• Stewart,W., 1968 Current-voltage characteristics of josephson junctions. Applied physics letters 12: 277–280.
• Takougang Kingni, S., G. Fautso Kuiate, R. Kengne, R. Tchitnga, and P. Woafo, 2017 Analysis of a no equilibrium linear resistive-capacitive-inductance shunted junction model, dynamics, synchronization, and application to digital cryptography in its fractional-order form. Complexity 2017.
• Whan, C., C. Lobb, and M. Forrester, 1995 Effect of inductance in externally shunted josephson tunnel junctions. Journal of applied physics 77: 382–389.
• Zhang, Z., K. Chau, Z. Wang, F. Li, and J. Li, 2011 Analysis of chaos in josephson junctions with external magnetic field for high-precision voltage measurement in electric vehicles. IEEE transactions on applied superconductivity 22: 4904704–4904704.