Home Phase synchronization of Wien bridge oscillator-based Josephson junction connected by hybrid synapse
Article
Licensed
Unlicensed Requires Authentication

Phase synchronization of Wien bridge oscillator-based Josephson junction connected by hybrid synapse

  • Cédric Noufozo Talonang , Alain Soup Tewa Kammogne EMAIL logo , Sundarapandian Vaidyanathan and Hilaire Bertrand Fotsin
Published/Copyright: August 2, 2022
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 77 Issue 12

Abstract

In this paper, a nonlinear Josephson junction (JJ) based-Wien bridge circuit is analyzed and coupled in order to obtain synchronization through passive components. The electrical equations governing the operation of our circuit are obtained using the laws of electrical circuit analysis. Chaotic phenomenon is demonstrated in the proposed circuit using relevant indicators such as the phase portraits, bifurcation and the corresponding Lyapunov diagram. Several coupling topologies are considered to achieve the phase synchronization that provides a better understanding of the distribution of energy in the overall system. Additionally, the effect of the noise is considered which considerably brings an added value to the dynamic of the phase synchronization between oscillators. Full synchronization is observed when the resistor is connected in parallel with the inductor or capacitor while different results are obtained when the resistor is connected in series with the capacitor or inductor. Finally, fine-tuning and selection of coupling coefficients reflects a migration toward synchronization between two Josephson junction based-Wien circuits that imply the self-adaptation of the synapse when two types of synapses are active simultaneously.

Keywords: Josephson junction; noise; phase synchronization; stability analysis; Wien bridge oscillator
Corresponding author: Alain Soup Tewa Kammogne, Laboratory of Condensed Matter, Electronics and Signal Processing (LAMACETS), Department of Physic, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] B. R. Andrievskii and A. L. Fradkov, “Control of chaos: methods and applications. I. Methods,” Autom. Rem. Control, vol. 64, no. 5, pp. 673–713, 2003. https://doi.org/10.1023/a:1023684619933.10.1023/A:1023684619933Search in Google Scholar

[2] A. S. Elwakil and A. M. Soliman, “Current conveyor chaos generators,” IEEE Trans. Circ. Syst. Fund. Theor. Appl., vol. 46, no. 3, pp. 393–398, 1999. https://doi.org/10.1109/81.751313.Search in Google Scholar

[3] M. Yassen, “Adaptive control and synchronization of a modified Chua’s circuit system,” Appl. Math. Comput., vol. 135, no. 1, pp. 113–128, 2003. https://doi.org/10.1016/s0096-3003(01)00318-6.Search in Google Scholar

[4] R. Mitra, G. Kaddoum, G. Dahman, and G. Poitau, “Performance analysis of information theoretic learning based cooperative localization,” IEEE Commun. Lett., vol. 25, no. 7, pp. 2196–2200, 2021. https://doi.org/10.1109/lcomm.2021.3068258.Search in Google Scholar

[5] S. Guan, C. H. Lai, and G. W. Wei, “Phase synchronization between two essentially different chaotic systems,” Phys. Rev., vol. 72, no. 1, p. 016205, 2005. https://doi.org/10.1103/physreve.72.016205.Search in Google Scholar PubMed

[6] I. Franović, K. Todorović, N. Vasović, and N. Burić, “Spontaneous formation of synchronization clusters in homogenous neuronal ensembles induced by noise and interaction delays,” Phys. Rev. Lett., vol. 108, no. 9, p. 094101, 2012. https://doi.org/10.1103/physrevlett.108.094101.Search in Google Scholar PubMed

[7] K. Segall, S. Guo, P. Crotty, D. Schult, and M. Miller, “Phase-flip bifurcation in a coupled Josephson junction neuron system,” Phys. B Condens. Matter, vol. 455, pp. 71–75, 2014. https://doi.org/10.1016/j.physb.2014.07.048.Search in Google Scholar

[8] B. A. Huberman, J. P. Crutchfield, and N. H. Packard, “Noise phenomena in Josephson junction,” Appl. Phys. Lett., vol. 37, pp. 750–752, 1980.10.1063/1.92020Search in Google Scholar

[9] P. Crotty, D. Schult, and K. Segall, “Josephson junction simulation of neurons,” Phys. Rev. E, vol. 82, p. 011914, 2010. https://doi.org/10.1103/physreve.82.011914.Search in Google Scholar

[10] Z. Liu, C. Wang, G. Zhang, and Y. Zhang, “Synchronization between neural circuits connected by hybrid synapse,” Int. J. Mod. Phys. B, vol. 33, no. 16, p. 1950170, 2019. https://doi.org/10.1142/s0217979219501704.Search in Google Scholar

[11] S. T. Kingni, K. Rajagopal, S. Çiçek, A. Cheukem, V. K. Tamba, and G. F. Kuiate, “Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation,” Eur. Phys. J. B, vol. 93, no. 3, pp. 1–11, 2020. https://doi.org/10.1140/epjb/e2020-100562-9.Search in Google Scholar

[12] F. C. Talla, R. Tchitnga, P. L. Fotso, R. Kengne, B. Nana, and A. Fomethe, “Unexpected behaviors in a single mesh Josephson junction based self-reproducing autonomous system,” Int. J. Bifurcat. Chaos, vol. 30, no. 07, p. 2050097, 2020. https://doi.org/10.1142/s0218127420500972.Search in Google Scholar

[13] S. Ma, P. Zhou, J. Ma, and C. Wang, “Phase synchronization of memristive systems by using saturation gain method,” Int. J. Mod. Phys. B, vol. 34, no. 09, p. 2050074, 2020. https://doi.org/10.1142/s0217979220500745.Search in Google Scholar

[14] D. R. Stinson, Cryptography: Theory and Practice, Boca Raton, Boca Raton, Taylor & Francis group, Chapman and Hall/CRC, 2005, pp. 1–84.10.1201/9781420057133Search in Google Scholar

[15] M. Rosenblum, A. Pikovsky, J. Kurths, C. Schäfer, and P. A. Tass, “Phase synchronization: from theory to data analysis,” in Handbook of Biological Physics, vol. 4, 2001st ed. North-Holland, Elsevier, 2001, pp. 279–321.10.1016/S1383-8121(01)80012-9Search in Google Scholar

[16] J. Feng, P. Yam, F. Austin, C. Xu, “Synchronizing the noise-perturbed Rössler hyperchaotic system via sliding mode control,” Z. Naturforsch., vol. 66, pp. 16–212, 2011. https://doi.org/10.5560/zna.2011.66a0006.Search in Google Scholar

[17] X. Y. Wang and H. Zhang, “A robust secondary secure communication scheme based on synchronization of spatiotemporal chaotic systems,” Z. Naturforsch., vol. 68, nos. 8–9, pp. 573–580, 2013. https://doi.org/10.5560/zna.2013-0046.Search in Google Scholar

[18] M. Varan, A. Akgül, E. Güleryüz, and K. Serbest, “Synchronisation and circuit realisation of chaotic Hartley system,” Z. Naturforsch., vol. 73, no. 6, pp. 521–531, 2018. https://doi.org/10.1515/zna-2018-0027.Search in Google Scholar

[19] T. L. Liao and S. H. Tsai, “Adaptive synchronization of chaotic systems and its application to secure communications,” Chaos, Solit. Fractals, vol. 11, no. 9, pp. 1387–1396, 2000. https://doi.org/10.1016/s0960-0779(99)00051-x.Search in Google Scholar

[20] G. M. Mahmoud and E. E. Mahmoud, “Complete synchronization of chaotic complex nonlinear systems with uncertain parameters,” Nonlinear Dynam., vol. 62, no. 4, pp. 875–882, 2010. https://doi.org/10.1007/s11071-010-9770-y.Search in Google Scholar

[21] K. S. T. Alain, A. T. Azar, F. H. Bertrand, and K. Romanic, “Robust observer-based synchronisation of chaotic oscillators with structural perturbations and input nonlinearity,” Int. J. Autom. Control, vol. 13, no. 4, pp. 387–412, 2019. https://doi.org/10.1504/ijaac.2019.10020237.Search in Google Scholar

[22] J. Fell and N. Axmacher, “The role of phase synchronization in memory processes,” Nat. Rev. Neurosci., vol. 12, no. 2, pp. 105–118, 2011. https://doi.org/10.1038/nrn2979.Search in Google Scholar PubMed

[23] S. Nobukawa, M. Kikuchi, and T. Takahashi, “Changes in functional connectivity dynamics with aging: a dynamical phase synchronization approach,” Neuroimage, vol. 188, pp. 357–368, 2019. https://doi.org/10.1016/j.neuroimage.2018.12.008.Search in Google Scholar PubMed

[24] T. Gao and Z. Zhao, “Multi-frequency phase synchronization,” in International Conference on Machine Learning, PMLR, 2019, pp. 2132–2141.Search in Google Scholar

[25] S. Mostaghimi, F. Nazarimehr, S. Jafari, and J. Ma, “Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow,” Appl. Math. Comput., vol. 348, pp. 42–56, 2019. https://doi.org/10.1016/j.amc.2018.11.030.Search in Google Scholar

[26] N. Wang, B. Bao, T. Jiang, M. Chen, and Q. Xu, “Parameter-independent dynamical behaviors in memristor-based Wien-bridge oscillator,” Math. Probl Eng., vol. 2017, pp. 1–14, 2017. https://doi.org/10.1155/2017/5897286.Search in Google Scholar

[27] B. Bao, T. Jiang, G. Wang, P. Jin, H. Bao, and M. Chen, “Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability,” Nonlinear Dynam., vol. 89, no. 2, pp. 1157–1171, 2017. https://doi.org/10.1007/s11071-017-3507-0.Search in Google Scholar

[28] H. Bao, N. Wang, B. Bao, M. Chen, P. Jin, and G. Wang, “Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria,” Commun. Nonlinear Sci. Numer. Simulat., vol. 57, pp. 264–275, 2018. https://doi.org/10.1016/j.cnsns.2017.10.001.Search in Google Scholar

[29] P. Louodop, R. Tchitnga, F. F. Fagundes, M. Kountchou, V. K. Tamba, and H. A. Cerdeira, “Extreme multistability in a Josephson-junction-based circuit,” Phys. Rev., vol. 99, no. 4, p. 042208, 2019. https://doi.org/10.1103/physreve.99.042208.Search in Google Scholar PubMed

[30] Q. Lai, P. D. K. Kuate, F. Liu, and H. H. C. Iu, “An extremely simple chaotic system with infinitely many coexisting attractors,” IEEE Trans. Circuits Syst. II Exp. Briefs, vol. 67, no. 6, pp. 1129–1133, 2019. https://doi.org/10.1109/tcsii.2019.2927371.Search in Google Scholar

[31] J. C. Sprott, “A proposed standard for the publication of new chaotic systems,” Int. J. Bifurcat. Chaos, vol. 21, no. 09, pp. 2391–2394, 2011. https://doi.org/10.1142/s021812741103009x.Search in Google Scholar

[32] Q. Xu, Q. Zhang, T. Jiang, B. Bao, and M. Chen, “Chaos in a second-order non-autonomous Wien-bridge oscillator without extra nonlinearity,” Circ. World, vol. 44, no. 3, pp. 108–114, 2018. https://doi.org/10.1108/cw-11-2017-0063.Search in Google Scholar

[33] A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, vol. 38, New York, Springer Science & Business Media, 2013, pp. 1–489.Search in Google Scholar

[34] Z. Yao, J. Ma, Y. Yao, and C. Wang, “Synchronization realization between two nonlinear circuits via an induction coil coupling,” Nonlinear Dynam., vol. 96, no. 1, pp. 205–217, 2019. https://doi.org/10.1007/s11071-019-04784-2.Search in Google Scholar

[35] Z. Zhu, G. Ren, X. Zhang, and J. Ma, “Effects of multiplicative-noise and coupling on synchronization in thermosensitive neural circuits,” Chaos, Solit. Fractals, vol. 151, p. 111203, 2021. https://doi.org/10.1016/j.chaos.2021.111203.Search in Google Scholar

[36] A. Olamat, P. Ozel, and A. Akan, “Synchronization analysis in epileptic EEG signals via state transfer networks based on visibility graph technique,” Int. J. Neural Syst., vol. 32, no. 02, p. 2150041, 2021. https://doi.org/10.1142/s0129065721500416.Search in Google Scholar

[37] B. A. Yao, Z., J. Ma, Y. Yao, and C. Wang, “Synchronization realization between two nonlinear circuits via an induction coil coupling,” Nonlinear Dynam., vol. 96, no. 1, pp. 205–217, 2019. https://doi.org/10.1007/s11071-019-04784-2.Search in Google Scholar

[38] K. Okuyama, H. J. Hartfuss, and K. H. Gundlach, “Distorted steps in the IV characteristic of Josephson junctions,” J. Low Temp. Phys., vol. 44, p. 283, 1981. https://doi.org/10.1007/bf00120778.Search in Google Scholar

[39] A. E. Botha, Y. M. Shukrinov, and M. R. Kolahchi, “Onset of chaos in intrinsic Josephson junctions,” Chaos, Solit. Fractals, vol. 48, pp. 32–37, 2013. https://doi.org/10.1016/j.chaos.2013.01.002.Search in Google Scholar

[40] K. Park, Y. C. Lai, S. Krishnamoorthy, and A. Kandangath, “Effect of common noise on phase synchronization in coupled chaotic oscillators,” Chaos, vol. 17, no. 1, p. 013105, 2007. https://doi.org/10.1063/1.2424423.Search in Google Scholar PubMed

Received: 2022-01-28
Accepted: 2022-06-23
Published Online: 2022-08-02
Published in Print: 2022-12-16

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. General
  3. The electrostatic wave modes and formation of dust voids in an externally magnetized cylindrical dusty plasma
  4. Atomic, Molecular & Chemical Physics
  5. Accurate theoretical calculation of relativistic atomic data of Zn-like, Ga-like and Ge-like Re ions
  6. Dynamical Systems & Nonlinear Phenomena
  7. Evolution of ion-acoustic shock waves in magnetized plasma with hybrid Cairns–Tsallis distributed electrons
  8. Free vibration analysis of rotating sandwich beams with FG-CNTRC face sheets in thermal environments with general boundary conditions
  9. Phase synchronization of Wien bridge oscillator-based Josephson junction connected by hybrid synapse
  10. Gravitation & Cosmology
  11. Formulation of axion-electrodynamics with Dirac fields
  12. Solid State Physics & Materials Science
  13. Tunable properties of the defect mode of a ternary photonic crystal with a high TC superconductor and semiconductor layers
  14. Trace cadmium ion detection using optical fiber Mach–Zehnder interferometer coated with PVA/TEOS/APTES
https://doi.org/10.1515/zna-2022-0024
Keywords for this article
Josephson junction; noise; phase synchronization; stability analysis; Wien bridge oscillator

Articles in the same Issue

  1. Frontmatter
  2. General
  3. The electrostatic wave modes and formation of dust voids in an externally magnetized cylindrical dusty plasma
  4. Atomic, Molecular & Chemical Physics
  5. Accurate theoretical calculation of relativistic atomic data of Zn-like, Ga-like and Ge-like Re ions
  6. Dynamical Systems & Nonlinear Phenomena
  7. Evolution of ion-acoustic shock waves in magnetized plasma with hybrid Cairns–Tsallis distributed electrons
  8. Free vibration analysis of rotating sandwich beams with FG-CNTRC face sheets in thermal environments with general boundary conditions
  9. Phase synchronization of Wien bridge oscillator-based Josephson junction connected by hybrid synapse
  10. Gravitation & Cosmology
  11. Formulation of axion-electrodynamics with Dirac fields
  12. Solid State Physics & Materials Science
  13. Tunable properties of the defect mode of a ternary photonic crystal with a high TC superconductor and semiconductor layers
  14. Trace cadmium ion detection using optical fiber Mach–Zehnder interferometer coated with PVA/TEOS/APTES
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 20.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2022-0024/html
Scroll to top button