Nonlinear Dynamics

, Volume 92, Issue 3, pp 1395–1402 | Cite as

Synchronous dynamics in neural system coupled with memristive synapse

  • Fei Xu
  • Jiqian ZhangEmail author
  • Tingting Fang
  • Shoufang Huang
  • Maosheng Wang
Original Paper


To study the collective behavior and the regulation mechanism of memristor, the Hindmarsh–Rose neuron cells are selected as the units to construct a coupled system by using the cubic flux-controlled memristor as a connecting synapses, both the firing mode and synchronous behavior in this coupled system are investigated. In this paper, a coefficient is introduced to describe the effect of electromagnetic induction of membrane potential, and the weights of synaptic connection between cells are selected as an adjustable parameter. We have found that, on the one hand, for the certain external current, the firing pattern of neurons could maintain normal state induced by proper electromagnetic induction, and the transition between different firing states could also be observed. On the other hand, both the synchronous effects could be effectively enhanced and the domain of synchronous parameters could be also expanded by tuning the electromagnetic parameters. Particularly, when the coupled system is in the synchronization state, one can see that the firing behavior of neurons will simultaneously change with the varying of the memristance. The similar phenomenon could also be found by introducing the external stimulus signal with a certain frequency. It means that the plasticity of biological synapses could be effectively mimicked by using the memristive synapse and thus the effective memory function of the memristor to the external stimulus signal may be realized. Above results may not only provide some useful clues for understanding the dynamic behavior of neural system coupled with memristive synapses, but also afford us some inspiration to simulate human brain memory, forgetting or some other functions by using the memristor neural network in the future.


Memristive synapse HR neuron Electromagnetic induction Synchronous dynamics Firing pattern transition 



The project supported by the Natural Science Foundation of Anhui Province, China (No. 1508085MA15), the Key project of cultivation of leading talents in Universities of Anhui Province (No. gxbjZD2016014), the Innovation and practice research project of graduate students of Anhui Normal University, China (No. 2017cxsj045), and the project of Academic and technical leaders candidate of Anhui Province (2017H117).

Compliance with ethical standards

Conflict of interest

The authors have declared that no competing interests exist. These authors contributed equally to this work.


  1. 1.
    Brette, R.: Computing with neural synchrony. PLoS Comput. Biol. 8, e1002561 (2012)CrossRefGoogle Scholar
  2. 2.
    Toutounji, H., Pipa, G.: Spatiotemporal computations of an excitable and plastic brain: neuronal plasticity leads to noise-robust and noise-constructive computations. PLoS Comput. Biol 10, e1003512 (2014)CrossRefGoogle Scholar
  3. 3.
    Liang, L.S., Zhang, J.Q., Liu, L.Z., et al.: Effect of topological connectivity on firing pattern transitions in coupled neurons. Chin. Phys. Lett. 31, 050502 (2014)CrossRefGoogle Scholar
  4. 4.
    Nicolelis, M.A.L., Baccala, L.A., Lin, R.C.S., et al.: Sensorimotor encoding by synchronous neural ensembly activity at multiple levels of the somatosensory system. Science 268, 1353–1358 (1995)CrossRefGoogle Scholar
  5. 5.
    Uhlhaas, P.J., Singer, W.: Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron 52, 155–168 (2006)CrossRefGoogle Scholar
  6. 6.
    Zhang, J.Q., Huang, S.F., Pang, S.T., et al.: Synchronization in the uncoupled neuron system. Chin. Phys. Lett. 32, 120502 (2015)CrossRefGoogle Scholar
  7. 7.
    Zhang, J.Q., Wang, C.D., Wang, M.S., et al.: Firing patterns transition induced by system size in coupled Hindmarsh–Rose neural system. Neurocomputing 74, 2961–2966 (2011)CrossRefGoogle Scholar
  8. 8.
    Luo, X.S., Qin, Y.H.: Random long-range connections induce activity of complex Hindmarsh–Rose neural networks. Physica A 387, 2155–2160 (2008)CrossRefGoogle Scholar
  9. 9.
    Wang, Z.Q., Xu, Y., Yang, H.: Lévy noise induced stochastic resonance in an FHN model. Sci. China Technol. Sci 59, 371–375 (2016)Google Scholar
  10. 10.
    Ma, J., Tang, J.: A review for dynamics of collective behaviors of network of neurons. Sci. China Technol. Sci 58, 2038–2045 (2015)CrossRefGoogle Scholar
  11. 11.
    Chua, L.: Memristor—the missing circuit element. IEEE Trans. Circuits Syst. 18, 507–519 (1971)Google Scholar
  12. 12.
    Strukov, D.B., Snider, G.S., Stewart, D.R., et al.: The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  13. 13.
    Lv, M., Wang, C.N., Ren, G.D., et al.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)CrossRefGoogle Scholar
  14. 14.
    Wu, J., Xu, Y., Ma, J.: Lévy noise improves the electrical activity in a neuron under electromagnetic radiation. PLoS ONE 12, e0174330 (2017)CrossRefGoogle Scholar
  15. 15.
    Wang, Y., Ma, J., Xu, Y., et al.: The electrical activity of neurons subject to electromagnetic induction and Gaussian white noise. Int. J. Bifurc. Chaos 27, 1750030 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Wu, F.Q., Wang, C.N., Jin, W.Y., et al.: Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Physica A 469, 81–88 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Xu, Y., Ying, H.P., Jia, Y., et al.: Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7, 43452 (2017)CrossRefGoogle Scholar
  18. 18.
    Ma, J., Wu, F.Q., Wang, C.N.: Synchronization behaviors of coupled neurons under electromagnetic radiation. Int. J. Mod. Phys. B. 31, 1650251 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Ma, J., Tang, J.: A review for dynamics in neuron and neuronal network. Nonlinear Dyn. 89, 1569–1578 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Ma, J., Lv, M., Zhou, P.: Phase synchronization between two neurons induced by coupling of electromagnetic field. Appl. Math. Comput. 307, 321–328 (2017)MathSciNetGoogle Scholar
  21. 21.
    Xu, Y., Jia, Y., Ma, J., et al.: Synchronization between neurons coupled by memristor. Chaos Soliton Fract. 104, 435–442 (2017)CrossRefGoogle Scholar
  22. 22.
    Li, Q.D., Tang, S., Zeng, H.Z., et al.: On hyperchaos in a small memristive neural network. Nonlinear Dyn. 78, 1087–1099 (2014)CrossRefzbMATHGoogle Scholar
  23. 23.
    Bao, B.C., Qian, H., Xu, Q., et al.: Coexisting behaviors of asymmetric attractors in hyperbolic-type memristor based Hopfield neural network. Front. Comput. Neurosci. 11, 1–14 (2017)CrossRefGoogle Scholar
  24. 24.
    Bao, B.C., Qian, H., Wang, J., et al.: Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network. Nonlinear Dyn. 90, 2359–2369 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Jo, S.H., Chang, T., Ebong, I., et al.: Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301 (2010)CrossRefGoogle Scholar
  26. 26.
    Pershin, Y.V., La Fontaine, S., Di Ventra, M.: Memristive model of amoeba learning. Phys. Rev. E 80, 021926 (2009)CrossRefGoogle Scholar
  27. 27.
    Corinto, F., Ascoli, A., Lanza, V., et al.: Memristor synaptic dynamics’ influence on synchronous behavior of two Hindmarsh–Rose neurons. In: The 2011 International Joint Conference on Neural Networks (IJCNN), pp. 2403–2408. IEEE (2011)Google Scholar
  28. 28.
    Ascoli, A., Tetzlaff, R., Lanza, V., et al.: Synchronization properties of a bio-inspired neural network. In: 2015 IEEE 15th International Conference on Nanotechnology (IEEE-NANO), pp. 621–624. IEEE (2015)Google Scholar
  29. 29.
    Ascoli, A., Lanza, V., Corinto, F., et al.: Synchronization conditions in simple memristor neural networks. J. Franklin Inst. 352, 3196–3220 (2015)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Thottil, S.K., Ignatius, R.P.: Nonlinear feedback coupling in Hindmarsh–Rose neurons. Nonlinear Dyn. 87, 1879–1899 (2017)CrossRefGoogle Scholar
  31. 31.
    Prodromakis, T., Phe, B.P., Papavassiliou, C., et al.: A versatile memristor model with nonlinear dopant kinetics. IEEE Trans. Electron. Dev. 58, 3099–3105 (2011)CrossRefGoogle Scholar
  32. 32.
    Hindmarsh, J.L., Rose, R.M.: A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B Bio. Sci 221, 87–102 (1984)CrossRefGoogle Scholar
  33. 33.
    Eguia, M.C., Rabinovich, M.I., Abarbanel, H.D.I.: Information transmission and recovery in neural communications channels. Phys. Rev. E. 62, 7111 (2000)CrossRefGoogle Scholar
  34. 34.
    Gonzálex-Miranda, J.M.: Complex bifurcation structures in the Hindmarsh–Rose neuron mode. Int. J. Bifurcat. Chaos 17, 3071–3083 (2007)CrossRefzbMATHGoogle Scholar
  35. 35.
    Bao, B.C., Wang, N., Xu, Q., et al.: A simple third-order memristive band pass filter chaotic circuit. IEEE Trans. Circuits Syst. II Express Briefs 99, 977–981 (2016). Google Scholar
  36. 36.
    Xu, Q., Lin, Y., Bao, B.C., Chen, M.: Multiple attractors in a non-ideal active voltage-controlled memristor based Chuas circuit. Chaos Solitons Fractals 83, 186–200 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Sukhodolsky, D.G., Leckman, J.F., Rothenberger, A., et al.: The role of abnormal neural oscillations in the pathophysiology of co-occurring Tourette syndrome and attention-deficit/hyperactivity disorder. Eur. Child Adolesc. Psychiatry 16, 51–59 (2007)CrossRefGoogle Scholar
  38. 38.
    Volman, V., Perc, M., Bazhenov, M.: Gap junctions and epileptic seizures-two sides of the same, coin? PLoS ONE 6, e20572 (2011)CrossRefGoogle Scholar
  39. 39.
    Song, X.L., Jin, W.Y., Ma, J.: Energy dependence on the electric activities of a neuron. Chin. Phys. B 24, 128710 (2015)CrossRefGoogle Scholar
  40. 40.
    Gonzalez-Sulser, A., Wang, J., Queenan, B.N., et al.: Hippocampal neuron firing and local field potentials in the in vitro 4-aminopyridine epilepsy model. J. Neurophysiol. 108, 2568–2580 (2012)CrossRefGoogle Scholar
  41. 41.
    Wang, H.X., Lu, Q.S., Wang, Q.Y.: Complete synchronization in coupled chaotic HR neurons with symmetric coupling schemes. Chin. Phys. Lett. 22, 2173 (2005)Google Scholar
  42. 42.
    Rakshit, S., Majhi, S., Bera, B.K., et al.: Time-varying multiplex network: intralayer and interlayer synchronization. Phys. Rev. E 96, 062308 (2017)CrossRefGoogle Scholar
  43. 43.
    Xu, Y., Li, Y., Zhang, H., et al.: The switch in a genetic toggle system with Lévy noise. Sci. Rep. 6, 31505 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Fei Xu
    • 1
  • Jiqian Zhang
    • 1
    Email author
  • Tingting Fang
    • 1
  • Shoufang Huang
    • 1
  • Maosheng Wang
    • 1
  1. 1.College of Physics and Electronic InformationAnhui Normal UniversityWuhuChina

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