Skip to main content
SpringerLink
Log in

A tristable locally active memristor and its application in Hopfield neural network

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

Abstract

This paper proposes a kind of nonvolatile locally active memristor. The three fingerprints for distinguishing memristor is verified by the stable and coexisting pinched hysteresis loops, when excited by bipolar periodical signal. The memristor has three stable equilibrium states, which can be mutually switched by injecting suitable voltage pulses. Therefore, it is considered as a three‐bit‐per‐cell memory device. Moreover, the locally active region can be adjusted by memristive parameter. Then, a neural network model composed of three Hopfield neurons is introduced, which is built by replacing one of the connecting synapses with the locally active memristor. It is found that the distribution of system equilibrium points depends on the coupling weight of memristor synapse. The bifurcation diagram reveals the coexistence phenomenon of multiple stable modes. In particular, when there exists a step difference between the natural frequency of the system and the external excitation frequency, complex bursting oscillation will emerge in the neural network. Finally, the equivalent hardware circuit is designed and implemented to confirm the results of numerical analysis, following commercial discrete components.

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Data availability

The data used to support the findings of this study are included within the article.

References

  1. Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory. 18, 507–519 (1971)

    Google Scholar 

  2. Mannan, Z.I., Choi, H., Rajamani, V., Kim, H., Chua, L.O.: Chua corsage memristor: phase portraits, basin of attraction, and coexisting pinched hysteresis loops. Int. J. Bifurc. Chaos 27(03), 1730011 (2017)

    MathSciNet  MATH  Google Scholar 

  3. Chua, L.O.: Five non-volatile memristor enigmas solved. Appl. Phys. A 124, 563 (2018)

    Google Scholar 

  4. Ma, J., Zhang, G., Hayat, T., Ren, G.D.: Model electrical activity of neuron under electric field. Nonlinear Dyn. 95, 1585–1598 (2019)

    Google Scholar 

  5. Wang, X.Y., Jin, C.X., Eshraghian, J.K., Lu, H.C., Ha, C.: A behavioral spice model of a binarized memristor for digital logic implementation. Circuits Syst. Signal Process. 40, 2682–2693 (2021)

    Google Scholar 

  6. Ramakrishnan, B., Durdu, A., Rajagopal, K., Akgul, A.: Infinite attractors in a chaotic circuit with exponential memristor and Josephson junction resonator. AEU Int. J. Electron. Commun. 123, 153319 (2020)

    Google Scholar 

  7. Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE. 64(2), 209–223 (1976)

    MathSciNet  Google Scholar 

  8. Chang, H., Zhen, W., Li, Y.X., Chen, G.R.: Dynamic analysis of a bi-stable bi-local active memristor and its associated oscillator system. Int. J. Bifur Chaos. 28(8), 1850105 (2018)

    MATH  Google Scholar 

  9. Li, C.L., Li, Z.Y., Feng, W., Tong, Y.N., Du, J.R., Wei, D.Q.: Dynamical behavior and image encryption application of a memristor-based circuit system. AEU-Int. J. Electron. Commun. 110, 152861 (2019)

    Google Scholar 

  10. Pham, V.T., Jafari, S., Vaidyanathan, S., Volos, C.K., Wang, X.: A novel memristive neural network with hidden attractors and its circuitry implementation. Sci. China Technol. Sci. 3, 358–363 (2016)

    Google Scholar 

  11. Chua, L.O.: Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)

    Google Scholar 

  12. Deng, Y., Li, Y.X.: Nonparametric bifurcation mechanism in 2-D hyperchaotic discrete memristor-based map. Nonlinear Dyn. 104, 4601–4614 (2021)

    Google Scholar 

  13. Strukov, D.B., Snider, G.S.: The missing memristor found. Nature 459, 1154 (2009)

    Google Scholar 

  14. Wang, Z., Qi, G.Y.: Modeling and analysis of a three-terminal-memristor-based conservative chaotic system. Entropy 23(1), 71 (2021)

    MathSciNet  Google Scholar 

  15. Zhu, B.M., Fan, Q.H., Li, G.Q., Wang, D.Q.: Chaos suppression for a buck converter with the memristive load. Analog. Integr. Circ. Syst. Signal Pr. 107, 309–318 (2021)

    Google Scholar 

  16. Sun, J.W., Han, J.T., Liu, P., Wang, Y.F.: Memristor-based neural network circuit of Pavlov associative memory with dual mode switching. AEU-Int. J. Electron. Commun. 129, 153552 (2020)

    Google Scholar 

  17. Yildirim, M., Kacar, F.: Chaotic circuit with OTA based memristor on image cryptology. AEU-Int. J. Electron. Commun. 127, 153490 (2020)

    Google Scholar 

  18. Zhang, Y., Wang, C.N., Tang, J., Ma, J., Ren, G.D.: Phase coupling synchronization of fhn neurons connected by a Josephson junction. Sci. China Tech. Sci. 11, 2328–2338 (2020)

    Google Scholar 

  19. Chua, L.O.: If it’s pinched it’s a memristor. Semicond. Sci. Tech. 29(10), 104001 (2014)

    Google Scholar 

  20. Dalitz, R.: From being to becoming. Phys. Bull. 32(11), 365–365 (1981)

    Google Scholar 

  21. Turing, A.: The chemical basis of morphogenesis. B Math. Biol. 237, 37–72 (1952)

    MathSciNet  MATH  Google Scholar 

  22. Chua, L.O.: Local activity is the origin of complexity. Int. J. Bifurc Chaos. 15(11), 3435–3456 (2011)

    MathSciNet  MATH  Google Scholar 

  23. Zhu, M.H., Wang, C.H., Deng, Q.L., Hong, Q.H.: Locally-active memristor with three coexisting pinched hysteresis loops and its emulator circuit. Int. J. Bifur Chaos. 30, 2050184 (2020)

    MathSciNet  MATH  Google Scholar 

  24. Li, C.L., Li, H.D., Xie, W.W., Du. J.R.: A S-type bi-stable locally-active memristor model and its analog implementation in an oscillator circuit. Nonlinear Dyn. (2021)

  25. Peng, Y.X., He, S.B., Sun, K.H.: Chaos in the discrete memristor-based system with fractional-order difference. Results Phys. 24, 104106 (2021)

    Google Scholar 

  26. Chua, L.O.: Memristor, hodgkin-huxley, and edge of chaos. Nanotechnology 24(38), 383001 (2013)

    Google Scholar 

  27. Mannan, Z.I., Adhikari, S.P., Kim, H., Chua, L.O.: Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci, Hopf bifurcation, and coexisting dynamic attractors. Nonlinear Dyn. 99, 3169–3196 (2021)

    Google Scholar 

  28. Mannan, Z.I., Yang, C.J., Kim, H.: Oscillation with 4-lobe chua corsage memristor. IEEE Circuits Syst. Mag. 18(2), 14–27 (2018)

    Google Scholar 

  29. Mannan, Z.I., Yang, C.J., Adhikari, S.P., Kim, H.: Exact analysis and physical realization of the 6-lobe chua corsage memristor. Complexity 2018, 1–21 (2018)

    Google Scholar 

  30. Li, C.L., Li, H.D., Xie, W.W., Du, J.R.: A S-type bistable locally active memristor model and its analog implementation in an oscillator circuit. Nonlinear Dyn. 106, 1041–1058 (2021)

    Google Scholar 

  31. Li, R.H., Wang, Z.H., Dong, E.Z.: A new locally-active memristive synapse coupled neuron model. Nonlinear Dyn. 104, 4459–4475 (2021)

    Google Scholar 

  32. Chang, H., Li, Y.X., Chen, G.R., Yuan, F.: Extreme multistability and complex dynamics of a memristor-based chaotic system. Int. J. Bifur. Chaos. 30, 434–445 (2020)

    MathSciNet  MATH  Google Scholar 

  33. Ascoli, A., Slesazeck, S., Mahne, H.: Nonlinear dynamics of a locally-active memristor. IEEE Trans. Circ. Syst. 62, 1165–1174 (2017)

    MathSciNet  MATH  Google Scholar 

  34. Ma, J., Tang, J.: A review for dynamics in neuron and neuronal network. Nonlinear Dyn. 89(3), 1569–1578 (2017)

    MathSciNet  Google Scholar 

  35. Kim, K., Eshraghian, K., Kang, H., Cho, K.: Nano-Crossbar Weighted memristor-based convolution neural network architecture for high-performance artificial intelligence applications. J. Nanosci. Nanotechnol. 21(3), 1833–1844 (2021)

    Google Scholar 

  36. Ma, C.G., Mou, J., Xiong, L., Banerjee, S., Liu, X.T., Han, X.: Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization. Nonlinear Dyn. 103, 2867–2880 (2021)

    Google Scholar 

  37. Aybar, I.K.: Memristor-based oscillatory behavior in the FitzHugh–Nagumo and Hindmarsh-Rose models. Nonlinear Dyn. 103, 2917–2929 (2021)

    Google Scholar 

  38. Ma, J., Wu, F.Q., Wang, C.N.: Synchronization behaviors of coupled neurons under electromagnetic radiation. Int. J. Mod. Phys. B 31(2), 1650251 (2016)

    MathSciNet  Google Scholar 

  39. Xiao, J.Y., Cheng, J., Shi, K.B., Zhang, R.M.: A general approach to fixed-time synchronization problem for fractional-order multi-dimension-valued fuzzy neural networks based on Memristor. IEEE Trans. Fuzzy Syst. 99, 3051308 (2021)

    Google Scholar 

  40. Tan, Y.M., Wang, C.H.: A simple locally-active memristor and its application in HR neurons. Chaos 30(5), 053118 (2020)

    MathSciNet  MATH  Google Scholar 

  41. Rostami, Z., Jafari, S.: Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction. Cogn. Neurodyn. 12, 235–254 (2018)

    Google Scholar 

  42. Xu, Y., Jia, Y., Ma, J., Alsaedi, A., Ahmad, B.: Synchronization between neurons coupled by memristor. Chaos Soliton Fract. 104, 435–442 (2017)

    Google Scholar 

  43. Haan, W.D., Flier, W., Koene, T., Scheltens, P., Stam, C.: Disrupted modular brain dynamics reflect cognitive dysfunction in Alzheimer’s disease. Neuroimage 59(4), 3085–3093 (2012)

    Google Scholar 

  44. Momani, S., Kumar, R., Srivastava, H.M., Kumar, S., Hadid, S.: A chaos study of fractional sir epidemic model of childhood diseases. Results Phys. 27, 104422 (2021)

    Google Scholar 

  45. Galiceanu, M., Mendes, C.F.O., Maciel, C., Beims, M.: Mechanisms to decrease the diseases spreading on generalized scale-free networks. Chaos 31(3), 033131 (2021)

    MathSciNet  Google Scholar 

  46. Pan, Y., Tsang, I., Lyu, Y., Singh, A., Lin, C.: Online mental fatigue monitoring via indirect brain dynamics evaluation. Neural Comput. (2021). https://doi.org/10.1162/neco_a_01382

    Article  MATH  Google Scholar 

  47. Hu, X.Y., Liu, C.X., Liu, L., Ni, J.K., Yao, Y.P.: Chaotic dynamics in a neural network under electromagnetic radiation. Nonlinear Dyn. 91, 1541–1554 (2018)

    Google Scholar 

  48. Liu, Y., Huang, X., Li, Y.X., Shen, H.: Multistability of hopfield neural networks with a designed discontinuous sawtooth-type activation function. Neural Comput. 455(5), 189–201 (2021)

    Google Scholar 

  49. Yu, F., Zhang, Z.N., Shen, H., Huang, Y.Y., Du, S.H.: Design and FPGA implementation of a pseudo-random number generator based on a Hopfield neural network under electromagnetic radiation. Front. Phys. 9, 690651 (2021)

    Google Scholar 

  50. Mannan, Z., Adhikari, S., Yang, C., Budhathoki, R., Kim, H., Chua, L.O.: Memristive imitation of synaptic transmission and plasticity. IEEE Trans. Neur. Net. Lear. 30, 3458–3470 (2019)

    Google Scholar 

  51. Xu, Y., Ying, H.P., Jia, Y., Ma, J., Hayat, T.: Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7, 43452 (2017)

    Google Scholar 

  52. Xu, F., Zhang, J.Q., Fang, T.T., Huang, S.F., Wang, M.: Synchronous dynamics in neural system coupled with memristive synapse. Nonlinear Dyn. 92(3), 1395–1402 (2018)

    Google Scholar 

  53. Bao, H., Hu, A.H., Liu, W.B., Bao, B.C.: Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Trans. Neur. Net. Lear. 31(2), 502–511 (2018)

    Google Scholar 

  54. Chua, L.O., Sbitnev, V., Kim, H.: Neurons are poised near the edge of chaos. Int. J. Bifur. Chaos. 22(04), 1250098 (2012)

    Google Scholar 

  55. Sah, M.P., Kim, H., Chua, L.O.: Brains are made of memristors. IEEE Circ. Syst. Mag. 14(1), 315–350 (2014)

    Google Scholar 

  56. Dong, Y.J., Wang, G.Y., Chen, G.R., Shen, Y., Ying, J.J.: A bi-stable nonvolatile locally-active memristor and its complex dynamics. Commun. Nonlinear Sci. Numer. Simul. 84, 105203 (2020)

    MathSciNet  MATH  Google Scholar 

  57. Joya, G., Atencia, M.A., Sandoval, F.: Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing 43, 219–237 (2002)

    MATH  Google Scholar 

  58. Wang, M., Li, J., Yu, S.S., Zhang, X., Li, Z., Iu, H.H.C.: A novel 3D non-autonomous system with parametrically excited abundant dynamics and bursting. Chaos 30, 043125 (2020)

    MathSciNet  MATH  Google Scholar 

  59. Brivio, S., Ly, D.R.B., Vianello, E., Spiga, S.: Non-linear memristive synaptic dynamics for efficient unsupervised learning in spiking neural networks. Front. Neurosc. 15, 580909 (2021)

    Google Scholar 

  60. Wen, Z.H., Li, Z.J., Li, X.: Bursting oscillations and bifurcation mechanism in memristor-based shimizu-morioka system with two time scales. Chaos Soliton Fract. 128, 58–70 (2019)

    MathSciNet  Google Scholar 

  61. Zhou, C.Y., Xie, F., Li, Z.J.: Complex bursting patterns and fast-slow analysis in a smallest chemical reaction system with two slow parametric excitations. Chaos Soliton Fract. 137, 109859 (2020)

    MathSciNet  MATH  Google Scholar 

  62. Njitacke, Z., Kengne, J.: Complex dynamics of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight: coexistence of multiple attractors and remerging feigenbaum trees. AEU-Int. J. Electron. Commun. 93, 242–252 (2018)

    Google Scholar 

  63. Njitacke, Z.T., Kengne, J., Fotsin, H.B.: A plethora of behaviors in a memristor based Hopfield neural networks (HNNs). Int. J. Dyn. Control. 7, 36–52 (2019)

    MathSciNet  Google Scholar 

  64. Wang, M.J., Liao, X.H., Deng, Y., Li, Z.J., Zeng, Y.C.: Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors. Chaos Soliton Fract. 130, 109406 (2020)

    MathSciNet  Google Scholar 

  65. Bao, B.C., Qian, H., Quan, X., Chen, M., Wang, J., Yu, Y.J.: Coexisting behaviors of asymmetric attractors in hyperbolic-type memristor based Hopfield neural network. Front. Comput. Neurosci. 11, 81 (2017)

    Google Scholar 

Download references

Funding

This work was supported by Hunan Provincial Natural Science Foundation of China (No. 2019JJ40109); Science and Technology Program of Hunan Province (No. 2019TP1014); research and innovation project of the graduate students of Hunan Institute of Science and Technology (No. YCX2020A336, No. YCX2021A08); Science and Research Creative Team of Hunan Institute of Science and Technology (No. 2019-TD-10); the Research Foundation of Education Bureau of Hunan Province of China (No. 21A0410).

Author information

Authors and Affiliations

  1. Key Laboratory of Hunan Province On Information Photonics and Freespace Optical Communications, College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang, 414006, China

    Chunlai Li, Yongyan Yang, Xuanbing Yang, Xiangyu Zi & Fanlong Xiao

  2. School of Computer Science & School of Cyberspace Science, Xiangtan University, Xiangtan, 411105, China

    Chunlai Li

Authors
  1. Chunlai Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongyan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuanbing Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiangyu Zi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fanlong Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunlai Li.

Ethics declarations

Conflict of interest

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Yang, Y., Yang, X. et al. A tristable locally active memristor and its application in Hopfield neural network. Nonlinear Dyn 108, 1697–1717 (2022). https://doi.org/10.1007/s11071-022-07268-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-07268-y

Keywords

Search

Navigation