Nonlinear Dynamics

, Volume 88, Issue 2, pp 893–901 | Cite as

Synchronization behavior of coupled neuron circuits composed of memristors

Original Paper

Abstract

The fluctuation of intracellular and extracellular ion concentration induces the variation of membrane potential, and also complex distribution of electromagnetic field is generated. Furthermore, the membrane potential can be modulated by time-varying electromagnetic field. Therefore, magnetic flux is proposed to model the effect of electromagnetic induction in case of complex electrical activities of cell, and memristor is used to connect the coupling between membrane potential and magnetic flux. Based on the improved neuron model with electromagnetic induction being considered, the bidirectional coupling-induced synchronization behaviors between two coupled neurons are investigated on Spice tool and also printed circuit board. It is found that electromagnetic induction is helpful for discharge of neurons under positive feedback coupling, while electromagnetic induction is necessary to enhance synchronization behaviors of coupled neurons under negative feedback coupling. The frequency analysis on isolate neuron confirms that the frequency spectrum is enlarged under electromagnetic induction, and self-induction effect is detected. These experimental results can be helpful for further dynamical analysis on synchronization of neuronal network subjected to electromagnetic radiation.

Keywords

Memristor Neuron Synchronization Electromagnetic induction 

References

  1. 1.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)CrossRefGoogle Scholar
  2. 2.
    Ader, C., Schneider, R., Hornig, S., et al.: A structural link between inactivation and block of a K\(^{+}\) channel. Nat. Struct. Molec. Biol. 15, 605–612 (2008)CrossRefGoogle Scholar
  3. 3.
    Fleidervish, I.A., Libman, L., Katz, E., et al.: Endogenous polyamines regulate cortical neuronal excitability by blocking voltage-gated Na\(^{+}\) channels. PNAS 105, 18994–18999 (2008)CrossRefGoogle Scholar
  4. 4.
    Gong, Y.B., Hao, Y.H., Xie, Y.H.: Channel block-optimized spiking activity of Hodgkin-Huxley neurons on random networks. Phys. A 389, 349–357 (2010)CrossRefGoogle Scholar
  5. 5.
    Liu, S.B., Wu, Y., Li, J.J., et al.: The dynamic behavior of spiral waves in stochastic Hodgkin-Huxley neuronal networks with ion channel blocks. Nonlinear Dyn. 73, 1055–1063 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ozer, M., Perc, M., Uzuntarla, M.: Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons. EPL 86, 40008 (2009)CrossRefGoogle Scholar
  7. 7.
    Wang, B.Y., Gong, Y.B.: Effects of channel noise on synchronization transitions in delayed scale-free network of stochastic Hodgkin-Huxley neurons. Chin. Phys. B 24, 0118702 (2014)CrossRefGoogle Scholar
  8. 8.
    Sun, X.J., Shi, X.: Effects of channel blocks on the spiking regularity in clustered neuronal networks. Sci. China Technol. Sci. 57, 884–897 (2014)Google Scholar
  9. 9.
    Huang, Y.D., Li, X., Shuai, J.W.: Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin-Huxley neurons. Chin. Phys. B 24, 120501 (2015)CrossRefGoogle Scholar
  10. 10.
    Qiu, K., Tang, J., Ma, J., et al.: Controlling intracellular Ca\(^{2+}\) spiral waves by the local agonist in the cell membrane. Chin. Phys. B 19, 030508 (2010)CrossRefGoogle Scholar
  11. 11.
    Hindmarsh, J.L., Rose, R.M.: A model of the nerve impulse using two first-order differential equations. Nature 296, 162–164 (1982)CrossRefGoogle Scholar
  12. 12.
    Herz, A.V.M., Gollisch, T., Machens, C.K., et al.: Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 314, 80–85 (2006)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Izhikevich, E.M.: Which model to use for cortical spiking neurons? IEEE Trans. Neural Netw. 15, 1063–1070 (2004)CrossRefGoogle Scholar
  14. 14.
    Gu, H.G., Pan, B.B.: A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model. Nonlinear Dyn. 81, 2107–2126 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ibarz, B., Casado, J.M., Sanjuán, M.A.F.: Map-based models in neuronal dynamics. Phys. Rep. 501, 1–74 (2011)CrossRefGoogle Scholar
  16. 16.
    Wang, C.N., He, Y.J., Ma, J., et al.: Parameters estimation, mixed synchronization, and antisynchronization in Chaotic Systems. Complexity 20, 64–73 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Ma, J., Xu, Y., Wang, C.N., et al.: Pattern selection and self-organization induced by random boundary initial values in a neuronal network. Phys. A 461, 586–594 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Song, X.L., Wang, C.N., Ma, J., et al.: Collapse of ordered spatial pattern in neuronal network. Phys. A 451, 95–112 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    Ma, J., Xu, J.: An introduction and guidance for neurodynamics. Sci. Bull. 60, 1969–1971 (2015)CrossRefGoogle Scholar
  21. 21.
    Wang, H.T., Chen, Y.: Firing dynamics of an autaptic neuron. Chin. Phys. B 24, 0128709 (2015)CrossRefGoogle Scholar
  22. 22.
    Song, X.L., Wang, C.N., Ma, J., et al.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Technol. Sci. 58, 1007–1014 (2015)CrossRefGoogle Scholar
  23. 23.
    Yilmaz, E., Baysal, V., Ozer, M., et al.: Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks. Phys. A 444, 538–546 (2016)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Herrmann, C.S., Klaus, A.: Autapse turns neuron into oscillator. Int. J. Bifurc. Chaos 14, 623–633 (2004)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Guo, D.Q., Chen, M.M., Perc, M., et al.: Firing regulation of fast-spiking interneurons by autaptic inhibition. EPL 114, 30001 (2016)CrossRefGoogle Scholar
  26. 26.
    Ren, G.D., Wu, G., Ma, J., et al.: Simulation of electric activity of neuron by setting up a reliable neuronal circuit driven by electric autapse. Acta Phys. Sin. 64, 058702 (2015)Google Scholar
  27. 27.
    Ma, J., Song, X.L., Jin, W.Y., et al.: Autapse-induced synchronization in a coupled neuronal network. Chaos Solitons Fract. 80, 31–38 (2015)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Ma, J., Qin, H.X., Song, X.L., et al.: Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int. J. Mod. Phys. B 29, 1450239 (2015)CrossRefGoogle Scholar
  29. 29.
    Qin, H.X., Wu, Y., Wang, C.N., et al.: Emitting waves from defects in network with autapses. Commun. Nonlinear Sci. Numer. Simulat. 23(1), 164–174 (2015)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Yi, G.S., Wang, J., Tsang, K.M., et al.: Spike-frequency adaptation of a two compartment neuron modulated by extracellular electric fields. Biol. Cybern. 109, 287–306 (2015)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Yi, G.S., Wang, J., Han, C.X., et al.: Spiking patterns of a minimal neuron to ELF sinusoidal electric field. Appl. Math. Model 36, 3673–3684 (2012)CrossRefGoogle Scholar
  32. 32.
    Akiyama, H., Shimizu, Y., Miyakawa, H., et al.: Extracellular DC electric fields induce nonuniform membrane polarization in rat hippocampal CA1 pyramidal neurons. Brain Res. 1383, 22–35 (2011)Google Scholar
  33. 33.
    Li, J.J., Liu, S.B., Liu, W.M., et al.: Suppression of firing activities in neuron and neurons of network induced by electromagnetic radiation. Nonlinear Dyn. 83, 801–810 (2016)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Lv, M., Ma, J.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)CrossRefGoogle Scholar
  35. 35.
    Lv, M., Ma, J.: Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205, 375–381 (2016)Google Scholar
  36. 36.
    Li, Q.D., Tang, S., Zeng, H.Z., et al.: On hyperchaos in a small memristive neural network. Nonlinear Dyn. 78, 1087–1099 (2014)CrossRefMATHGoogle Scholar
  37. 37.
    Pham, V.T., Jafari, S., Vaidyanathan, S., et al.: A novel memristive neural network with hidden attractors and its circuitry implementation. Sci. China Technol. Sci. 59, 358–363 (2016)CrossRefGoogle Scholar
  38. 38.
    Cafagna, D., Grassi, G.: On the simplest fractional-order memristor-based chaotic system. Nonlinear Dyn. 70, 1185–1197 (2012)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Yuan, F., Wang, G.Y., Wang, X.Y.: Dynamical characteristics of an HP memristor based on an equivalent circuit model in a chaotic oscillator. Chin. Phys. B 24, 060506 (2015)CrossRefGoogle Scholar
  40. 40.
    Ma, J., Chen, Z.Q., Wang, Z.L., et al.: A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium. Nonlinear Dyn. 81, 1275–1288 (2015)CrossRefMATHGoogle Scholar
  41. 41.
    Chen, M., Li, M.Y., Yu, Q., et al.: Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit. Nonlinear Dyn. 81, 215–226 (2015)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Sabarathinam, S., Volos, C.K., Thamilmaran, K.: Implementation and study of the nonlinear dynamics of a memristor-based duffing oscillator. Nonlinear Dyn. (2016). doi:10.1007/s11071-016-3022-8

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  2. 2.NAAM-Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations