Skip to main content
SpringerLink
Log in

Switching bifurcation of a Rulkov neuron system with ReLu-type memristor

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, the flow switching theory is utilized to discuss the complex switching dynamics of a nonautonomous Rulkov neuron system with a ReLU-type memristor, and the conditions under which crossing and grazing motions of the Rulkov neuron system occur at the boundary are analyzed. Multistability of nonlinear system at the separation boundaries is revealed by the coexisting bifurcation diagrams, coexisting phase planes, and dual-parameter maps. A set of attractors in the case of the coexisting periodic and chaotic motions are studied by means of the simulation results of the trajectory mapping. Furthermore, field programmable gate array is utilized to design the Rulkov neuron system hardware experiments, and the experimental outcomes of the hardware implementations validate the numerical results.

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data availability

The datasets supporting the conclusions of this article are included within the article and its additional files.

References

  1. Sun, J.W., Liu, P., Wen, S.P., Wang, Y.F., Wang, Y.Y.: Memristor-based neural network circuit with multimode generalization and differentiation on pavlov associative memory. IEEE Trans. Cybern. 53(5), 3351–3362 (2023)

    Article  PubMed  Google Scholar 

  2. Yang, F.F., Ren, G.D., Tang, J.: Dynamics in a memristive neuron under an electromagnetic field. Nonlinear Dyn. 111(23), 21917 (2023)

    Article  Google Scholar 

  3. Lin, H.R., Wang, C.H., Cui, L., Sun, Y.C., Yu, F., Xu, C.: Brain-like initial-boosted hyperchaos and application in biomedical image encryption. IEEE Trans. Ind. Inform. 18(2), 8839–8850 (2022)

    Article  Google Scholar 

  4. Zhang, X.T., Liu, J., Wang, D., Liu, H.J.: Geometric control and synchronization of a complex-valued laser chain network. Nonlinear Dyn. 111(7), 6395–6410 (2023)

    Article  Google Scholar 

  5. Hodgkin, A.L., Huxley, A.F.: Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. 116, 449–472 (1952)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. Bull. Math. Biol. 52(1–2), 25–71 (1990)

    Article  CAS  PubMed  Google Scholar 

  7. Zhang, S., Zheng, J.H., Wang, X.P., Zeng, Z.G.: A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability. Chaos Solitons Fractals 145, 110761 (2021)

    Article  MathSciNet  Google Scholar 

  8. Connor, J.A., Stevens, C.F.: Prediction of repetitive firing behaviour from voltage clamp data on an isolated neuron soma. J. Physio. 213(1), 31–53 (1971)

    Article  CAS  Google Scholar 

  9. Karthikeyan, A., Moroz, I., Rajagopal, K., Duraisamy, P.: Effect of temperature sensitive ion channels on the single and multilayer network behavior of an excitable media with electromagnetic induction. Chaos Solitons Fractals 150, 111144 (2022)

    Article  MathSciNet  Google Scholar 

  10. Wu, F.Q., Gu, H.G., Jia, Y.B.: Bifurcations underlying different excitability transitions modulated by excitatory and inhibitory memristor and chemical autapses. Chaos Solitons Fractals 153, 111611 (2021)

    Article  MathSciNet  Google Scholar 

  11. Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  12. Pu, J.R., Goh, W.L., Nambiar, V.P., Chong, Y.S., Do, A.T.: A low-cost high-throughput digital design of biorealistic spiking neuron. IEEE Trans. Circuits Syst. 68(4), 1398–1402 (2021)

    Article  Google Scholar 

  13. Chen, M., Luo, X.F., Suo, Y.H., Xu, Q., Wu, H.G.: Hidden extreme multistability and synchronicity of memristor-coupled non-autonomous memristive Fitzhugh-Nagumo models. Nonlinear Dyn. 111(8), 7773–7788 (2023)

    Article  Google Scholar 

  14. Wu, F.Q., Wang, C.N., Xu, Y., Ma, J.: Model of electrical activity in cardiac tissue under electromagnetic induction. Sci. Rep. 6, 28 (2016)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  15. Rulkov, N.F.: Modeling of spiking-bursting neural behavior using two-dimensional map. Phys. Rev. E 65(4), 041922 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  16. Li, K.X., Bao, H., Li, H.Z., Ma, J., Hua, Z.Y., Bao, B.C.: Memristive Rulkov neuron model with magnetic induction effects. IEEE Trans. Ind. Inform. 18(3), 1726–1736 (2022)

    Article  Google Scholar 

  17. Xu, Q., Liu, T., Feng, C.T., Bao, H., Wu, H.G., Bao, B.C.: Continuous non-autonomous memristive Rulkov model with extreme multistability. Chin. Phys. B 30(12), 128702 (2022)

    Article  ADS  Google Scholar 

  18. Wu, F.Q., Meng, H., Ma, J.: Reproduced neuron-like excitability and bursting synchronization of memristive Josephson junctions loaded inductor. Neural Netw. 169, 607–621 (2024)

    Article  PubMed  Google Scholar 

  19. Ma, M.L., Xiong, K.L., Li, Z.J., He, S.B.: Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk. Chin. Phys. B. (2023). https://doi.org/10.1088/1674-1056/aceee9

    Article  Google Scholar 

  20. Lu, J.Y., Xie, X.H., Lu, Y.P., Wu, Y.L., Li, C.L., Ma, M.L.: Dynamical behaviors in discrete memristor-coupled small-world neuronal networks. Chin. Phys. B 12, 10246 (2023)

    Google Scholar 

  21. Yang, F.F., Ma, J.: Creation of memristive synapse connection to neurons for keeping energy balance. Pramana J. Phys. 97(2), 55 (2023)

    Article  ADS  Google Scholar 

  22. Li, C.L., Yang, Y.Y., Yang, X.B., Zi, X.Y., Xiao, F.L.: A tristable locally active memristor and its application in Hopfield neural network. Nonlinear Dyn. 108(2), 1697–1717 (2022)

    Article  Google Scholar 

  23. Wei, L.X., Li, D.: Stochastic morris-lecar model with time delay under magnetic field excitation. Chaos Solitons Fractals 173, 113715 (2023)

    Article  MathSciNet  Google Scholar 

  24. Ding, D.W., Chen, X.Y., Yang, Z.L., Zhang, H.W., Zhang, X.: Coexisting multiple firing behaviors of fractional-order memristor-coupled HR neuron considering synaptic crosstalk and its ARM-based implementation. Chaos Solitons Fractals 158, 112014 (2022)

    Article  MathSciNet  Google Scholar 

  25. Yang, F., Wang, Y., Ma, J.: An adaptive synchronization approach in a network composed of four neurons with energy diversity. Indian J. Phys. 97(7), 2125–2137 (2023)

    Article  ADS  CAS  Google Scholar 

  26. Chen, C.J., Min, F.H.: ReLU-type memristor-based hopfield neural network. Eur. Phys. J Spec. Top. 231(16–17), 2979–2992 (2022)

    Article  Google Scholar 

  27. Zhang, Y.Z., Peng, D., Chen, C.J., Zhao, G.Z., Zhang, X.Q.: Initial-condition effects on ReLU-type hyper-jerk system and its application in image encryption. Phys. Scr. 98(9), 095252 (2023)

    Article  ADS  Google Scholar 

  28. Chen, C.J., Min, F.H., Zhang, Y.Z., Bao, H.: ReLU-type Hopfield neural network with analog hardware implementation. Chaos Solitons Fractals 167, 113068 (2023)

    Article  Google Scholar 

  29. Chen, C.J., Min, F.H., Hu, F., Cai, J.M., Zhang, Y.Z.: Analog/digital circuit simplification for Hopfield neural network. Chaos Solitons Fractals 173, 113727 (2023)

    Article  Google Scholar 

  30. Luo, A.C.J.: A theory for flow switchability in discontinuous dynamical systems. Nonlinear Anal. Hybrid Syst. 2(4), 1030–1061 (2008)

    Article  MathSciNet  Google Scholar 

  31. Min, F.H., Zhang, W., Ji, Z.Y., Zhang, L.: Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor. Chaos Solitons Fractals 152, 111369 (2021)

    Article  MathSciNet  Google Scholar 

  32. Min, F.H., Rui, Z.: Boundary dynamics of a non-smooth memristive Hindmarsh-Rose neuron system. Chaos 32(10), 103117 (2022)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China under Grant No. 61971228.

Author information

Authors and Affiliations

  1. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210023, China

    Fuhong Min, Guanghui Zhai, Sipeng Yin & Junsheng Zhong

Authors
  1. Fuhong Min
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guanghui Zhai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sipeng Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Junsheng Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fuhong Min.

Ethics declarations

Conflict of interest

Compliance with ethical standards. The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Min, F., Zhai, G., Yin, S. et al. Switching bifurcation of a Rulkov neuron system with ReLu-type memristor. Nonlinear Dyn 112, 5687–5706 (2024). https://doi.org/10.1007/s11071-024-09335-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-024-09335-y

Keywords

Search

Navigation