Skip to main content
SpringerLink
Log in

Dynamical analysis of Josephson junction neuron model driven by a thermal signal and its digital implementation based on microcontroller

  • Regular Article - Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The dynamical features and the digital implementation of a microcontroller Josephson junction neuron model driven by a thermal signal is investigated in this paper. By designing the system above as a thermistor in series to some variant voltage source connected in parallel to a resistor and a capacitor, we show that the hysteresis loop appearances are strongly temperature and applied voltage source dependent. We further determine the equilibrium points of the model system while studying their stability. Following the numerical analysis, we find out the existence of period-1-oscillations, continuous spiking oscillations, periodic bursting oscillations, and chaotic oscillations in the neural activities as functions of the temperature and modulation parameters of the sinusoidal voltage source. As an illustration, we implement some digital system measurements in view of discussing deeply the previous findings while providing their physical implications.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: ...].

References

  1. F. Grassia, T. Kohno, T. Levi, Digital implementation of stochastic two-dimensional neuron model. J. Physiol. 110, 409–416 (2016)

    Google Scholar 

  2. C.J. Schwiening, A brief historical perspective: Hodgkin and Huxley. J. Physiol. 590, 2571–2575 (2012)

    Article  Google Scholar 

  3. E.M. Izhikevich, Simple model of spinking neurous. IEEET Trans. Neural Netw. 15, 1063–1070 (2004)

    Article  Google Scholar 

  4. C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35, 193–213 (1981)

    Article  ADS  Google Scholar 

  5. H. Gu, Biological experimental observations of an unnoticed chaos as simulated by the Hindmarsh -Rose model. PLoS One 8, e81759–e81770 (2013)

    Article  ADS  Google Scholar 

  6. Y. Liu, W.J. Xu, J. Ma, F. Alzahrani, A. Hobiny, A new photosensitive neuron model and its dynamics. Front. Inform. Technol. Electron. Eng. 21, 1387–1396 (2020)

    Article  Google Scholar 

  7. T.R. Chay, J. Rinzel, Bursting, beating, and chaos in an excitable membrane model. Biophys. J . 47, 357–366 (1985)

    Article  Google Scholar 

  8. M. Kawato, Cable properties of a neuron model with non-uniform membrane resistivity. J. Theor. Biol. 111, 149–169 (1984)

    Article  ADS  Google Scholar 

  9. S. Guo, C. Wang, J. Ma et al., Transmission of blocked electric pulses in a cable neuron model by using an electric field. Neurocomputing 216, 627–637 (2016)

    Article  Google Scholar 

  10. H.S. Seung, D.D. Lee, Y.B. Reis et al., The autapse: A simple illustration of short-term analog memory storage by tuned synaptic feedback. J. Comput. Neurosci. 9, 171–185 (2000)

    Article  Google Scholar 

  11. M. Lv, C. Wang, G. Ren et al., Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)

    Article  Google Scholar 

  12. W.Y. Jin, A. Wang, J. Ma et al., Effects of electromagnetic induction and noise on the regulation of sleep wake cycle. Sci. China Technol. Sci. 62, 2113–2119 (2019)

    Article  ADS  Google Scholar 

  13. F.Q. Wu, J. Ma, G. Zhang, Energy estimation and coupling synchronization between biophysical neurons. Sci. China Technol. Sci. 63, 625–636 (2020)

    Article  ADS  Google Scholar 

  14. J. Ma, J. Tang, A review for dynamics of collective behaviors of network of neurons. Sci. China Technol. Sci. 58, 2038–20045 (2015)

    Article  ADS  Google Scholar 

  15. Y.P. Lin, C.H. Bennett, T. Cabaret et al., Physical realization of a supervised learning system built with organic memristive synapses. Sci. Rep. 6, 31932–31943 (2016)

    Article  ADS  Google Scholar 

  16. A. Afifi, A. Ayatollahi, F. Raissi et al., Efficient hybrid CMOS-Nano circuit design for spiking neurons and memristive synapses with STDP, IEICE Trans. Fund. Electron. Commun. Comput. Sci. 93, 1670–1677 (2010)

    Google Scholar 

  17. B. Bao, A. Hu, H. Bao, Q. Xu, M. Chen, H. Wu, Three-dimensional memristive Hindmarsh-rose neuron model with hidden coexisting asymmetric behaviors. Complexity (2018). https://doi.org/10.1155/2018/3872573

    Article  Google Scholar 

  18. B. Bao, H. Qian, Q. Xu, M. Chen, J. Wang, Y. Yu, Coexisting behaviors of asymmetric attractors in hyperbolictype memristor based hopfeld neural network. Front. Comput. Neurosci. 11, 81–94 (2018)

    Article  Google Scholar 

  19. Y. Xu, M. Liu, Z. Zhu, J. Ma, Dynamics and coherence resonance in a thermosensitive neuron driven by photocurrent. Chin. Phys. B 29, 098704–098715 (2020)

    Article  ADS  Google Scholar 

  20. T. Nakayama, Thermosensitive neurons in the brain. Jpn. J. Physiol. 35, 375–389 (1985)

    Article  Google Scholar 

  21. Y. Xua, Y. Guo, G. Ren, M. Jua, Dynamics and stochastic resonance in a thermosensitive neuron. Appl. Math. Comput. 385, 125427–125439 (2020)

    MathSciNet  MATH  Google Scholar 

  22. Y. Liu, W.-J. Xu, J. Ma, F. Alzahrani, A. Hobiny, A new photosensitive neuron model and its dynamics. Front. Inf. Technol. Electr. Eng. 21, 1387–1396 (2020)

    Article  Google Scholar 

  23. Z. Yao, P. Zhou, Z. Zhu, J. Ma, Phase synchronization between a light-dependent neuron and a thermosensitive neuron. Neurocomputing 423, 518–534 (2021)

    Article  Google Scholar 

  24. Q. Xu, X. Tan, D. Zhu, H. Bao, B. Bao, Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit. Chaos, Solitons Fractals 141, 110353 (2020)

    Article  MathSciNet  Google Scholar 

  25. E.M. Izhikevich, Simple model of spiking neurons. IEEE Trans. Neural Netw. 14, 1569–1572 (2003)

    Article  Google Scholar 

  26. Y. Liu, Q. Huang, Z. Wei, Dynamics at infinity and Jacobi stability of trajectories for the Yang-Chen system. Discret. Contin. Dyn. Syst. Ser. B 26, 3357–3380 (2021)

    Article  MathSciNet  Google Scholar 

  27. A. Mishra, S. Ghosh, S.K. Dana, T. Kapitaniak, C. Hens, Neuron-like spiking and bursting in Josephson junctions: A review. Chaos 31, 052101–052108 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  28. K.S. Ojo, A.O. Adelakun, A.A. Oluyinka, excitable Josephson junctions, Synchronisation of cyclic coupled Josephson junctions and its microcontroller-based implementation. Pramana-J. Phys. 92(77), 92–98 (2019)

    Google Scholar 

  29. F. Wang, T. Liu, N.V. Kuznetsov, Z. Wei, Jacobi stability analysis and the onset of chaos in a two-degree-of-freedom mechanical system. Int. J. Bifurc. Chaos 31, 2150075 (2021)

    Article  MathSciNet  Google Scholar 

  30. P. Crotty, K. Segall, D. Aschult, Modeling biological neurons with Josephson junctions. BMC Neurosci. 10, 44–44 (2009)

    Article  Google Scholar 

  31. P. Crotty, D. Schult, K. Segall, Josephson junction simulation of neurons. Phys. Rev. E 82, 011914–011921 (2010)

    Article  ADS  Google Scholar 

  32. Y. Zhang, N.C. Wang, J. Tang et al., Phase coupling synchronization of FHN neurons connected by a Josephson junction. Sci. China Technol. Sci. 63, 2328–2338 (2020)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is partially funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India via funding number CIT/CNS/2021/RD/064.

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

    Noel Freddy Fotie Foka

  2. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, 600069, Tamilnadu, India

    Balamurali Ramakrishnan & Karthikeyan Rajagopal

  3. Department of Rural Engineering, Faculty of Agronomy and Agricultural Sciences, University of Dschang, P. O Box 222, Dschang, Cameroon

    André Rodrigue Tchamda

  4. Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Sifeu Takougang Kingni

  5. National Advanced School of Engineering, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon

    Victor Kamgang Kuetche

Authors
  1. Noel Freddy Fotie Foka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Balamurali Ramakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. André Rodrigue Tchamda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sifeu Takougang Kingni
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Karthikeyan Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Victor Kamgang Kuetche
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

NFFF and BR developed the model and theoretically analyzed the rate equations of the proposed model. ART and STK did the digital implementation of the proposed model. KR and VK Kuetche participated in the data analysis at different stages. All authors contributed to the interpretation of the results and writing of the manuscript.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Foka, N.F.F., Ramakrishnan, B., Tchamda, A.R. et al. Dynamical analysis of Josephson junction neuron model driven by a thermal signal and its digital implementation based on microcontroller. Eur. Phys. J. B 94, 234 (2021). https://doi.org/10.1140/epjb/s10051-021-00256-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00256-y

Search

Navigation