Skip to main content
SpringerLink
Log in

Propagation characteristics of weak signal in feedforward Izhikevich neural networks

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

Abstract

The feedforward neural network is widely applied in various machine learning architectures, in which the synaptic weight between layers plays an important role in the weak signal propagation. In this paper, the five-layer Izhikevich neural networks with excitatory or excitatory–inhibition neurons are employed to study the effect of Gaussian white noise and synaptic weight between layers on the weak signal transmission characteristics of the subthreshold excitatory postsynaptic currents signal imposed on the input layer. It can be found that there is an optimum value of noise intensity (a medium noise intensity) at which the weak signal can be stably propagated in the five-layer Izhikevich neural networks. The spike timing precision (STP) under the optimal noise intensity will become maximum by increasing the synaptic weight. The noise intensity and synaptic weight corresponding to the maximum value of the STP in the excitatory–inhibition network are smaller than those in excitatory–inhibition network. For the smaller or the bigger noise intensity, however, the STP will become very small, and the weak signal cannot be transmitted from the input layer to the output layer. Furthermore, the weak signal is propagated from the input layer to the output layer and enhanced under a larger synaptic weight in the feedforward 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

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

References

  1. 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 

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

    Google Scholar 

  3. Litvak, V., Sompolinsky, H., Segev, I., Abeles, M.: On the transmission of rate code in long feedforward networks with excitatory–inhibitory balance. J. Neurosci. 23, 3006–3015 (2003)

    Google Scholar 

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

    Google Scholar 

  5. Feinerman, O., Segal, M., Moses, E.: Signal propagation along unidimensional neuronal networks. J. Neurophysiol. 94, 3406–3416 (2005)

    Google Scholar 

  6. Feinerman, O., Moses, E.: Transport of information along unidimensional layered networks of dissociated hippocampal neurons and implications for rate coding. J. Neurosci. 26, 4526–4534 (2006)

    Google Scholar 

  7. August, D.A., Levy, W.B.: Temporal sequence compression by an integrate-and-fire model of hippocampal area CA3. J. Comput. Neurosci. 6, 71–90 (1999)

    Google Scholar 

  8. Lee, A.K., Wilson, M.A.: Memory of sequential experience in the hippocampus during slow wave sleep. Neuron 36, 1183–1194 (2002)

    Google Scholar 

  9. Qin, Y.M., Wang, J., Men, C., Deng, B., Wei, X.L.: Vibrational resonance in feedforward network. Chaos 21, 023133 (2011)

    Google Scholar 

  10. Men, C., Wang, J., Qin, Y.M., Deng, B., Tsang, K.M., Chan, W.L.: Propagation of spiking regularity and double coherence resonance in feedforward networks. Chaos 22, 013104 (2012)

    Google Scholar 

  11. Gao, Y., Wang, J.: Oscillation propagation in neural networks with different topologies. Phys. Rev. E 83, 031909 (2011)

    Google Scholar 

  12. Faisal, A.A., Selen, L.P.J., Wolpert, D.M.: Noise in the nervous system. Nat. Rev. Neurosci. 9, 292–303 (2008)

    Google Scholar 

  13. Softky, W., Koch, C.: The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334–350 (1993)

    Google Scholar 

  14. Qin, Y., Wang, J., Men, C., Deng, B., Wei, X., Yu, H.: The effects of time delay on the stochastic resonance in feed-forward-loop neuronal network motifs. Commun. Nonlinear Sci. 19(4), 3660–3670 (2014)

    Google Scholar 

  15. Collins, J.J., Chow, C.C., Imhoff, T.T.: Stochastic resonance without tuning. Nature 376, 236–238 (1995)

    Google Scholar 

  16. Eichwald, C., Walleczek, J.: Aperiodic stochastic resonance with chaotic input signals in excitable systems. Phys. Rev. E 55, 6315–6318 (1997)

    Google Scholar 

  17. Perc, M.: Noise-induced spatial periodicity in excitable chemical media. Chem. Phys. Lett. 410, 49–53 (2005)

    Google Scholar 

  18. Perc, M.: Stochastic resonance on excitable small-world networks via a pacemaker. Phys. Rev. E 76, 066203 (2007)

    Google Scholar 

  19. Parmananda, P., Santos, G., Escalera, J., Rivera, M., Showalter, K.: Stochastic resonance of electrochemical aperiodic spike trains. Phys. Rev. E 71, 031110 (2005)

    Google Scholar 

  20. Yilmaz, E., Baysal, V., Perc, M., Ozer, M.: Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network. Sci. China Technol. Sci. 59, 364–370 (2016)

    Google Scholar 

  21. Perc, M.: Stochastic resonance on excitable small-world networks via a pacemaker. Phys. Rev. E 76(2), 066203 (2007)

    Google Scholar 

  22. Yilmaz, E., Uzuntarla, M., Ozer, M., Perc, M.: Stochastic resonance in hybrid scale-free neuronal networks. Phys. A 392(22), 5735–5741 (2013)

    Google Scholar 

  23. Hornic, K.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359–366 (1989)

    Google Scholar 

  24. Ozer, M., Perc, M., Uzuntarla, M., Koklukaya, E.: Weak signal propagation through noisy feedforward neuronal networks. Neuroreport 21, 338–43 (2010)

    Google Scholar 

  25. Jeyakumari, S., Chinnathambi, V., Rajasekar, S., et al.: Single and multiple vibrational resonance in a quintic oscillator with monostable potentials. Phys. Rev. E 80(2), 046608 (2009)

    Google Scholar 

  26. Yilmaz, E., Baysal, V., Ozer, M., Perc, M.: Autaptic pacemaker mediated propagation of weak rhythmic, activity across small-world neuronal networks. Phys. A 444, 538–546 (2016)

    Google Scholar 

  27. Ullner, E., Zaikin, A., Garcıa-Ojalvo, J., Bascones, R., Kurths, J.: Vibrational resonance and vibrational propagation in excitable systems. Phys. Let. A 312(5), 348–354 (2003)

    Google Scholar 

  28. Deng, B., Wang, J., Wei, X.: Effect of chemical synapse on vibrational resonance in coupled neurons. Chaos 19(1), 013117 (2009)

    Google Scholar 

  29. Eichwald, C., Walleczek, J.: Aperiodic stochastic resonance with chaotic input signals in excitable systems. Phys. Rev. E. 55, 6315–6318 (1997)

    Google Scholar 

  30. Wang, H.T., Chen, Y.: Response of autaptic Hodgkin–Huxley neuron with noise to subthreshold sinusoidal signals. Phys. A 462, 321–329 (2016)

    Google Scholar 

  31. Sun, X.J., Liu, Z.F.: Combined effects of time delay and noise on the ability of neuronal network to detect the subthreshold signal. Nonlinear Dyn. 92(4), 1707–1717 (2018)

    Google Scholar 

  32. Yao, Y.G., Yang, L.J., Wang, C.J., Liu, Q., Gui, R., Xiong, J., et al.: Subthreshold periodic signal detection by bounded noise-induced resonance in the FitzHugh–Nagumo neuron. Complexity 2018, 5632650 (2018)

    Google Scholar 

  33. Arredondo, L.T., Perez, C.A.: Spatially coincident vibrotactile noise improves subthreshold stimulus detection. PLoS ONE 12, e0186932 (2017)

    Google Scholar 

  34. Whittington, M.A., Jefferys, J.G.R.: Recurrent excitatory postsynaptic potentials induced by synchronized fast cortical oscillations. Proc. Natl. Acad. Sci. 94, 12198–12203 (1997)

    Google Scholar 

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

    Google Scholar 

  36. Clark, K.A., Collingridge, G.L.: Synaptic potentiation of dual-component excitatory postsynaptic currents in the rat hippocampus. J. Physiol. 482, 39–52 (1995)

    Google Scholar 

  37. Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 4(6), 1569–1572 (2003)

    Google Scholar 

  38. Ren, G., Xue, Y., Lia, Y., Ma, J.: Field coupling benefits signal exchange between Colpitts systems. Appl. Math. Comput. 342, 45–54 (2019)

    Google Scholar 

  39. Guo, D.Q., Li, C.G.: Stochastic and coherence resonance in feedforward-loop neuronal network motifs. Phy. Rev. E 79(5), 051921 (2009)

    Google Scholar 

  40. Jiang, X., Liu, C., Wang, J.: Delay-induced multiple vibrational resonance in the bi-fan neuronal network motifs. BMEI 7, 288–296 (2014)

    Google Scholar 

  41. Ge, M., Jia, Y., Kirunda, J.B., Xu, Y., Shen, J., Lu, L., et al.: Propagation of firing rate by synchronization in a feed-forward multilayer Hindmarsh–Rose neural network. Neurocomputing 320, 60–68 (2018)

    Google Scholar 

  42. Ge, M., Xu, Y., Zhang, Z., et al.: Autaptic modulation-induced neuronal electrical activities and wave propagation on network under electromagnetic induction. Eur. Phys. J. Spec. Top. 227, 799–809 (2018)

    Google Scholar 

  43. Lu, L., Jia, Y., Kirunda, J.B., et al.: 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 

  44. Hansel, D., Mato, G., Meunier, C.: Phase dynamics for weakly coupled Hodgkin–Huxley neurons. EPL 23(5), 367–372 (1993)

    Google Scholar 

  45. Destexhe, A., Mainen, Z.F., Sejnowski, T.J.: Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J. Comput. Neurosci. 1, 195–230 (1994)

    Google Scholar 

  46. Yang, L., Jia, Y., Yi, M.: The effects of electrical coupling on the temporal coding of neural signal in noisy Hodgkin-Huxley neuron ensemble. In: Sixth international conference on natural computation, vol 2, pp 819–823 (2010)

  47. 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 (1996)

    Google Scholar 

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

    Google Scholar 

  49. Lu, L., Jia, Y., Xu, Y., Ge, M., Yang, L., Zhan, X.: Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction. Sci. China Technol. Sci. 62, 427–440 (2019)

    Google Scholar 

  50. Xu, Y., Jia, Y., Ma, J., Hayat, T., Alsaedi, A.: Collective responses in electrical activities of neurons under field coupling. Sci. Rep. 8, 1349 (2018)

    Google Scholar 

  51. Ge, M., Jia, Y., Xu, Y., Yang, L.: Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn. 91(1), 515–523 (2018)

    Google Scholar 

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

    Google Scholar 

  53. Rostamia, Z., Pham, V.-T., Jafari, S., Hadaeghic, F., Ma, J.: Taking control of initiated propagating wave in a neuronal network using magnetic radiation. Appl. Math. Comput. 338, 141–151 (2018)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  56. Xu, Y., Ma, J., Zhan, X., Yang, L., Jia, Y.: Temperature effect on memristive ion channels. Cogn. Neurodyn. (2019). https://doi.org/10.1007/s11571-019-09547-8

    Google Scholar 

  57. 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)

    Google Scholar 

  58. Yilmaz, E., Ozer, M., Baysal, V., Perc, M.: Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Sci. Rep. 6, 30914 (2016)

    Google Scholar 

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

    Google Scholar 

  60. Yao, Z., Ma, J., Yao, Y., Wang, C.: Synchronization realization between two nonlinear circuits via an induction coil coupling. Nonlinear Dyn. 96, 205–217 (2019)

    Google Scholar 

  61. Ma, J., Wu, F., Alsaedi, A., Tang, J.: Crack synchronization of chaotic circuits under field coupling. Nonlinear Dyn. 93, 2057–2069 (2018)

    Google Scholar 

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

    Google Scholar 

  63. Handa, H., Sharma, B.B.: Synchronization of a set of coupled chaotic FitzHugh–Nagumo and Hindmarsh–Rose neurons with external electrical stimulation. Nonlinear Dyn. 85, 1–16 (2016)

    Google Scholar 

  64. Baltanas, J.P., Caado, J.M.: Noise-induced resonances in the Hindmarsh–Rose neuronal model. Phys. Rev. E 65, 041915 (2002)

    Google Scholar 

  65. Xu, Y., Jia, Y., Kirunda, J.B., et al.: Dynamic behaviors in coupled neurons system with the excitatory and inhibitory autapse under electromagnetic induction. Complexity 2018, 3012743 (2018)

    Google Scholar 

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

    Google Scholar 

Download references

Acknowledgements

This study was supported by the National Natural Science Foundation of China under Grant under Nos. 11775091 (Y.J.) and 11704140 (Y.Z.); the Natural Science Foundation of Hubei Province under No. 2017CFB116 (Y.Z.).

Author information

Authors and Affiliations

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

    Mengyan Ge, Ya Jia, Lulu Lu, Ying Xu, Huiwen Wang & Yunjie Zhao

Authors
  1. Mengyan Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya Jia
    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. Ying Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huiwen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yunjie Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya Jia.

Ethics declarations

Conflict of interest

The authors declare that they have no potential 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

Ge, M., Jia, Y., Lu, L. et al. Propagation characteristics of weak signal in feedforward Izhikevich neural networks. Nonlinear Dyn 99, 2355–2367 (2020). https://doi.org/10.1007/s11071-019-05392-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05392-w

Keywords

Search

Navigation