Skip to main content
SpringerLink
Log in

Study on propagation efficiency and fidelity of subthreshold signal in feed-forward hybrid neural network under electromagnetic radiation

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

Abstract

The hybrid neural model provides a computationally effective and biophysics-based neuron behavior model, which maintains its simplicity by incorporating the dynamics characteristics of ion channels in two fast ion channels. In view of the issue of signal propagation in multilayer network composed of hybrid neurons is still unclear and the role of neural network is mainly used to generate biological consciousness and help creatures to think and act, it is necessary to explore neural network with more perfect function and better transmission efficiency. Considering a feed-forward neural network (FFN) which is composed of hybrid neurons in the presence of electromagnetic radiation, the effects of the Gaussian white noise, the strength of synaptic weight and inter-layer connection probability on subthreshold excitatory postsynaptic current (EPSC) propagation are investigated. In order to clarify the mechanism of signal transmission more clearly, the dot raster plot of spike and the corresponding post-spike time histogram of each layer are explored. Particularly, the propagation efficiency and fidelity of subthreshold EPSC signal in the FFN are investigated by calculating the power norm and the spike timing precision. Our results indicate that both the power norm and the spike timing precision fluctuate with the increase in the inter-layer connection probability, and the multi-periods bursting discharge mode can be detected in both the transmission layers and the output layer. Besides, there exists an optimal noise intensity to guarantee the best temporal coding and maximum transmission efficiency of subthreshold EPSC signal. Moreover, the optimal noise intensity makes the fidelity of the FFN the highest, which ensures that the weak signal and the excitation caused by noise can be distinguished. The conclusions obtained in this paper have potential value for discussing the encoding, decoding and propagation mechanism of information in real neural networks.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Lewis, E.R.: The elements of single neurons: a review. IEEE Trans. Syst. Man Cybern. 13, 702–710 (2012)

    Google Scholar 

  2. Liu, Y., Li, C.: Stochastic resonance in feedforward-loop neuronal network motifs in astrocyte field. J. Theor. Biol. 335, 265–275 (2013)

    MathSciNet  MATH  Google Scholar 

  3. Qin, Y., Wang, J., Men, C., Deng, B., Wei, X., Yu, H., Chan, W.L.: Stochastic resonance in feedforward acupuncture networks. Commun. Nonlinear. Sci. 19, 3660–3670 (2014)

    MathSciNet  MATH  Google Scholar 

  4. Guo, D.: A survey of signal propagation in feedforward neuronal networks. In: International Symposium on Neural Networks. Springer, Berlin, Heidelberg (2011)

  5. Finke, C., Jürgen, V., Postnova, S., Braun, H.A.: Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations. Math. Biosci. 214, 109–121 (2008)

    MathSciNet  MATH  Google Scholar 

  6. Huber, M.T., Braun, H.A.: Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and related spike generation. Biosystems. 89, 38–43 (2007)

    Google Scholar 

  7. Wang, G., Xu, D., Cheng, Q.: Influences of correlated colored-noises on logistic model for tree growth. Acta Phys. Sin. 62, 224208 (2013)

    Google Scholar 

  8. Guo, D., Li, C.: Signal propagation in feedforward neuronal networks with unreliable synapses. J. Comput. Neurosci. 30, 567–587 (2011)

    MathSciNet  MATH  Google Scholar 

  9. Wang, S., Wang, W., Liu, F.: Propagation of firing rate in a feed-forward neuronal network. Phys. Rev. Lett. 96, 018103 (2006)

    Google Scholar 

  10. Li, J., Yu, W., Xu, D., Liu, F., Wang, W.: Mechanism for propagation of rate signals through a 10-layer feedforward neuronal network. Chin. Phys. B. 18, 5560 (2009)

    Google Scholar 

  11. Reyes, A.D.: Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nat. Neurosci. 6, 593–599 (2003)

    Google Scholar 

  12. Kumar, A., Rotter, S., Aertsen, A.: Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding. Nat. Rev. Neurosci. 11, 615–627 (2010)

    Google Scholar 

  13. Gerrit, J.C., Amir, Z., Carlo, G., Rene, V.L.: A real-time hybrid neuron network for highly parallel cognitive systems. In: Annual International Conference on the IEEE Engineering in Medicine and Biology Society, vol. 2016, pp. 792–795 (2016)

  14. Alex, A., Albert, D., Jurgen, K., Yamir, M., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469, 93–153 (2008)

    MathSciNet  Google Scholar 

  15. Ge, M., Wang, G., Jia, Y.: Influence of the Gaussian colored noise and electromagnetic radiation on the propagation of subthreshold signals in feedforward neural networks. Sci. China Technol. Sci. (2020). https://doi.org/10.1007/s11431-020-1696-8

    Article  Google Scholar 

  16. Lu, L., Jia, Y., Kirunda, J.B., Xu, Y., Ge, M., Pei, Q., Yang, L.: Effects of noise and synaptic weight on propagation of subthreshold excitatory postsynaptic current signal in a feed-forward neural network. Nonlinear Dyn. 95, 1673–1686 (2019)

    Google Scholar 

  17. Wang, G., Xu, Y., Ge, M., Lu, L., Jia, Y.: Mode transition and energy dependence of FitzHugh–Nagumo neural model driven by high-low frequency electromagnetic radiation. AEU Int. J. Electron. Commun. 120, 153209 (2020)

    Google Scholar 

  18. Wilson, H.R.: Simplified dynamics of human and mammalian neocortical neurons. J. Theor. Biol. 200, 375–388 (1999)

    Google Scholar 

  19. Zhao, X., Kim, J.W., Robinson, P.A., Rennie, C.J.: Low dimensional model of bursting neurons. J. Comput. Neurosci. 36, 81–95 (2014)

    MathSciNet  Google Scholar 

  20. Liu, Y., Ma, J., Xu, Y., Jia, Y.: Electrical mode transition of hybrid neuronal model induced by external stimulus and electromagnetic induction. Int. J. Bifurc. Chaos 29, 1950156 (2019)

    MathSciNet  MATH  Google Scholar 

  21. Lv, M., Ma, J., Yao, Y., Faris, A.: Synchronization and wave propagation in neuronal network under field coupling. Sci. China Technol. Sci. 62, 448–457 (2019)

    Google Scholar 

  22. Zhou, X., Xu, Y., Wang, G., Jia, Y.: Ionic channel blockage in stochastic Hodgkin–Huxley neuronal model driven by multiple oscillatory signals. Cogn. Neurodyn. 14, 569–578 (2020)

    Google Scholar 

  23. Yi, M., Yang, L.: Propagation of firing rate by synchronization and coherence of firing pattern in a feed-forward multilayer neural network. Phys. Rev. E 81, 061924 (2010)

    Google Scholar 

  24. Lv, M., Wang, C., Ren, G., Ma, J., Song, X.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)

    Google Scholar 

  25. Xu, Y., Jia, Y., Ma, J., Tasawar, H., Ahmed, A.: Collective responses in electrical activities of neurons under field coupling. Sci. Rep. 8, 1349 (2018)

    Google Scholar 

  26. Akihisa, T., Tetsushi, U., Shigeki, T.: Bifurcation analysis of Izhikevich model. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 16, 849–862 (2009)

    MathSciNet  MATH  Google Scholar 

  27. Tanabe, S., Sato, S., Pakdaman, K.: Response of an ensemble of noisy neuron models to a single input. Phys. Rev. E 60, 7235–7238 (1999)

    Google Scholar 

  28. Breen, B., Gerken, W., Robert, J.: Hybrid integrate-and-fire model of a bursting neuron. Neural Comput. 15, 2843–2862 (2003)

    MATH  Google Scholar 

  29. Liu, Q., Ye, W., Hu, N., Cai, H., Yu, H., Wang, P.: Olfactory receptor cells respond to odors in a tissue and semiconductor hybrid neuron chip. Biosens. Bioelectron. 26, 1672–1678 (2011)

    Google Scholar 

  30. Thibeault, C., Narayan, S.: Using a hybrid neuron in physiologically inspired models of the basal ganglia. Front. Comput. Neurosci. 7, 88 (2013)

    Google Scholar 

  31. Hashimoto, S., Torikai, H.: A novel hybrid spiking neuron: bifurcations, responses, and on-chip learning. IEEE Trans. Circuit Syst. 57, 2168–2181 (2010)

    MathSciNet  Google Scholar 

  32. Hindmarsh, J.L., Rose, R.M.: A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B. 221, 87–102 (1984)

    Google Scholar 

  33. Liu, C., Wang, J., Yu, H., Deng, B., Tsang, K.M., Chan, W.L., Wong, Y.K.: The effects of time delay on the stochastic resonance in feed-forward-loop neuronal network motifs. Commun. Nonlinear Sci. 19, 1088–1096 (2014)

    MathSciNet  MATH  Google Scholar 

  34. Qin, H., Ma, J., Ren, G., Zhou, P.: Field coupling-induced wave propagation and pattern stability in a two-layer neuronal network under noise. Int. J. Mod. Phys. B 32, 1850298 (2018)

    MATH  Google Scholar 

  35. Peercy, B.E.: Initiation and propagation of a neuronal intracellular calcium wave. J. Comput. Neurosci. 25, 334–348 (2008)

    MathSciNet  Google Scholar 

  36. Al-Basha, D., Prescott, S.A.: Intermittent failure of spike propagation in primary afferent neurons during tactile stimulation. J. Neurosci. 39, 9927–9939 (2019)

    Google Scholar 

  37. Xue, M., Atallah, B.V., Scanziani, M.: Equalizing excitation-inhibition ratios across visual cortical neurons. Nature 511, 596–600 (2014)

    Google Scholar 

  38. Guo, D., Perc, M., Zhang, Y., Xu, P., Yao, D.: Frequency-difference-dependent stochastic resonance in neural systems. Phys. Rev. E 96, 022415 (2017)

    Google Scholar 

  39. Hopfield, J.J.: Pattern recognition computation using action potential timing for stimulus representation. Nature 376, 33–36 (1995)

    Google Scholar 

  40. Ofer, F., Menahem, S., Elisha, M.: Signal propagation along unidimensional neuronal networks. J. Neurophysiol. 94, 3406 (2005)

    Google Scholar 

  41. Huber, M.T., Braun, H.A.: Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation. Phys. Rev. E 73, 041929 (2006)

    Google Scholar 

  42. Yuichi, S., Shin, I.: Stochastic resonance with differential code in feedforward network with intra-layer random connections. Neural Netw. 19, 469–476 (2006)

    MATH  Google Scholar 

  43. Ma, J., Song, X., Tang, J., Wang, C.: Wave emitting and propagation induced by autapse in a forward feedback neuronal network. Neurocomput. PLoS Comput. Biol. 167, 378–389 (2015)

    Google Scholar 

  44. Rinberg, A., Taylor, A.L., Marder, E.: The effects of temperature on the stability of a neuronal oscillator. PLoS Comput. Biol. 9, e1002857 (2013)

    Google Scholar 

  45. Andrew, R.D., Dudek, F.E.: Analysis of intracellularly recorded phasic bursting by mammalian neuroendocrine cells. J. Neurophysiol. 51, 552 (1984)

    Google Scholar 

  46. Pei, X., Wilkens, L., Moss, F.: Noise-mediated spike timing precision from aperiodic stimuli in an array of Hodgekin–Huxley-type neurons. Phys. Rev. Lett. 77, 4679–4682 (1996)

    Google Scholar 

  47. Ali, C., Ugur, I., Muhammet, U., Mahmut, O.: Vibrational resonance in feed-forward-loop neuronal network motifs. BMC Neurosci. 16, 189–190 (2015)

    Google Scholar 

  48. Ozer, M., Perc, M., Uzuntarla, M., Koklukaya, E.: Weak signal propagation through noisy feedforward neuronal networks. NeuroReport 21, 338–343 (2010)

    Google Scholar 

  49. Postma, E.O., van den Herik, H.J., Hudson, P.T.: Robust feedforward processing in synfire chains. Int. J. Neural Syst. 7, 537–542 (1996)

    Google Scholar 

  50. Diesmann, M., Gewaltig, M., Aertsen, A.: Stable propagation of synchronous spiking in cortical neural networks. Nature 402, 529–533 (1999)

    Google Scholar 

  51. Wang, J., Han, R., Wei, X., Qin, Y., Yu, H., Deng, B.: Weak signal detection and propagation in diluted feed-forward neural network with recurrent excitation and inhibition. Int. J. Mod. Phys. B 30, 1550253 (2016)

    MathSciNet  Google Scholar 

  52. Yu, Y., Liu, F., Wang, J., Wang, W.: Spike timing precision for a neuronal array with periodic signal. Phys. Lett. A 282, 23–30 (2001)

    MathSciNet  MATH  Google Scholar 

  53. Shimokawa, T., Rogel, A., Pakdaman, K., Sato, S.: Stochastic resonance and spike-timing precision in an ensemble of leaky integrate and fire neuron models. Phys. Rev. E 59, 3461–3470 (1999)

    Google Scholar 

  54. Wang, Z., Tian, C., Dhamala, M., Liu, Z.: A small change in neuronal network topology can induce explosive synchronization transition and activity propagation in the entire network. Sci. Rep. 7, 561–565 (2017)

    Google Scholar 

  55. Zhao, J., Qin, Y., Che, Y.: Effects of Sine–Wiener noise on signal propagation in a randomly connected neural network. Phys. A 533, 122030 (2019)

    Google Scholar 

  56. Zhang, X., Huang, H., Li, P., Wu, F., Wu, W., Jiang, M.: Propagation of spiking and burst-spiking synchronous states in a feed-forward neuronal network. Chin. Phys. Lett. 29, 120501 (2012)

    Google Scholar 

  57. Ma, J., Wu, F., Hayat, T., Zhou, P., Tang, J.: Electromagnetic induction and radiation-induced abnormality of wave propagation in excitable media. Phys. A 486, 508–516 (2017)

    MathSciNet  Google Scholar 

  58. Ge, M., Xu, Y., Zhang, Z., Peng, Y., Kang, W., Yang, L., Jia, Y.: Autaptic modulation-induced neuronal electrical activities and wave propagation on network under electromagnetic induction. Eur. Phys. J. 227, 799–809 (2018)

    Google Scholar 

  59. Ge, M., Jia, Y., Kirunda, J.B., Xu, Y., Shen, J., Lu, L., Liu, Y., Pei, Q., Zhan, X., Yang, L.: Propagation of firing rate by synchronization in a feed-forward multilayer Hindmarsh–Rose neural network. Neurocomputing 320, 60–68 (2018)

    Google Scholar 

  60. Ge, M., Jia, Y., Xu, Y., Lu, L., Wang, H., Zhao, Y.: Wave propagation and synchronization induced by chemical autapse in chain Hindmarsh–Rose neural network. Appl. Math. Comput. 352, 136–145 (2019)

    MathSciNet  MATH  Google Scholar 

  61. Ge, M., Jia, Y., Lu, L., Xu, Y., Zhao, Y.: Propagation characteristics of weak signal in feedforward Izhikevich neural networks. Nonlinear Dyn. 99, 2355–2367 (2020)

    Google Scholar 

  62. Lima, P.M., Ford, N.J., Lumb, P.M.: Computational methods for a mathematical model of propagation of nerve impulses in myelinated axons. Appl. Numer. Math. 85, 38–53 (2014)

    MathSciNet  MATH  Google Scholar 

  63. Rajagopal, K., Moroz, I., Karthikeyan, A., Duraisamy, P.: Wave propagation in a network of extended Morris–Lecar neurons with electromagnetic induction and its local kinetics. Nonlinear Dyn. 100, 3625–3644 (2020)

    Google Scholar 

  64. Huang, H., Robert, M.M., Yao, W.: A simplified neuronal model for the instigation and propagation of cortical spreading depression. Adv. Appl. Math. Mech. 3, 759–773 (2011)

    MathSciNet  MATH  Google Scholar 

  65. Rosas, A., Lindenberg, K.: Pulse propagation in chains with nonlinear interactions. Phys. Rev. E 69, 016615 (2004)

    Google Scholar 

  66. Michele, C., Mauro, F.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 2, 73–85 (2015)

    Google Scholar 

  67. Vinaya, M., Ignatius, R.P.: Electromagnetic radiation from memristor applied to basal ganglia helps in controlling absence seizures. Nonlinear Dyn. 101, 1–12 (2020)

    Google Scholar 

  68. Ratas, I., Pyragas, K.: Effect of high-frequency stimulation on nerve pulse propagation in the FitzHugh–Nagumo model. Nonlinear Dyn. 67, 2899–2908 (2012)

    MathSciNet  Google Scholar 

  69. Xu, Y., Jia, Y., Kirunda, J.B., Shen, J., Ge, M., Lu, L., Pei, Q.: Dynamic behaviors in coupled neurons system with the excitatory and inhibitory autapse under electromagnetic induction. Complexity 2018, 3012743 (2018)

    Google Scholar 

  70. Lu, L., Bao, C., Ge, M., Xu, Y., Yang, L., Zhan, X., Jia, Y.: Phase noise-induced coherence resonance in three dimension memristive Hindmarsh–Rose neuron model. Eur. Phys. J. Spec. Top. 228, 2101–2110 (2019)

    Google Scholar 

  71. Xu, Y., Jia, Y., Wang, H., Liu, Y., Wang, P., Zhao, Y.: Spiking activities in chain neural network driven by channel noise with field coupling. Nonlinear Dyn. 95, 3237–3247 (2019)

    MATH  Google Scholar 

  72. Ge, M., Lu, L., Xu, Y., Mamatimin, R., Pei, Q., Jia, Y.: Vibrational mono- / bi-resonance and wave propagation in FitzHugh–Nagumo neural systems under electromagnetic induction. Chaos Solitons Fractal 133, 109645 (2020)

    MathSciNet  Google Scholar 

  73. Lu, L., Jia, Y., Ge, M., Xu, Y., Li, A.: Inverse stochastic resonance in Hodgkin–Huxley neural system driven by Gaussian and non-Gaussian colored noises. Nonlinear Dyn. 100, 877–889 (2020)

    Google Scholar 

  74. Hou, Z., Ma, J., Zhan, X., Yang, L., Jia, Y.: Estimate the electrical activity in a neuron under depolarization field. Chaos Solitons Fractals 142, 110522 (2020)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This project is supported by National Natural Science Foundation of China under Grants Nos. 11775091 and 11704140, and the self-determined research funds of CCNU from the college’ basic research and operation of MOE under No. CCNU20TS004.

Author information

Authors and Affiliations

  1. Institute of Biophysics and Department of Physics, Central China Normal University, Wuhan, 430079, China

    Guowei Wang, Mengyan Ge, Lulu Lu, Ya Jia & Yunjie Zhao

Authors
  1. Guowei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mengyan Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lulu Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ya Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yunjie Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunjie Zhao.

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

Wang, G., Ge, M., Lu, L. et al. Study on propagation efficiency and fidelity of subthreshold signal in feed-forward hybrid neural network under electromagnetic radiation. Nonlinear Dyn 103, 2627–2643 (2021). https://doi.org/10.1007/s11071-021-06247-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06247-z

Keywords

Search

Navigation