Simulation of a Chaos-Like Irregular Neural Firing Pattern Based on Improved Deterministic Chay Model

  • Zhongting Jiang
  • Dong WangEmail author
  • Jin Sun
  • Hengyue Shi
  • Huijie Shang
  • Yuehui Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11554)


In this paper, the deterministic Chay model was improved considering the generation mechanism of an action potential, with special relevance to the opening of potassium channel after depolarization. Then a chaos-like irregular non-periodic neural firing pattern, which was lying between period n and period (n + 1) bursting in a period-adding bifurcation and composed of alternating period n and period (n + 1) bursts, was also simulated by this improved Chay model. The nonlinear time series analysis results suggest this pattern display both deterministic and stochastic dynamic characteristics, as same as those results in the previous studies. This pattern was always simulated by stochastic neuron models and considered to be coherence resonance near the bifurcation points induced by the inner noise. However, there was no noise in this improved deterministic Chay model. This present paper attempted to discuss and preliminarily explain the generation mechanism of this firing pattern from the standpoint of the unification of certainty and randomness.


Neural discharge activity Deterministic Chay model Action potential Chaos-like Neural firing pattern 



This research was supported by the Shandong Provincial Natural Science Foundation, China (No. ZR2018LF005), the National Key Research and Development Program of China (No. 2016YFC0106000), the Natural Science Foundation of China (Grant No. 61302128, 61573166, 61572230), and the Youth Science and Technology Star Program of Jinan City (201406003).


  1. 1.
    Khurana, V., Kumar, P., Saini, R., Roy, P.P.: EEG based word familiarity using features and frequency bands combination. Cogn. Syst. Res. 49, 33–48 (2018)CrossRefGoogle Scholar
  2. 2.
    Huaguang, G., Zhiguo, Z., Bing, J., Shenggen, C.: Dynamics of on-off neural firing patterns and stochastic effects near a sub-critical Hopf bifurcation. PLoS ONE 10(4), e0121028 (2015)CrossRefGoogle Scholar
  3. 3.
    Li, C.H., Yang, S.Y.: Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of Hindmarsh-Rose neurons. Appl. Math. Model. 39(21), 6631–6644 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Shi, R., Hu, G., Wang, S.: Reconstructing nonlinear networks subject to fast-varying noises by using linearization with expanded variables. Commun. Nonlinear Sci. Numer. Simul. 72, 407–416 (2019)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhao, Z., Gu, H.: Identifying time delay-induced multiple synchronous behaviours in inhibitory coupled bursting neurons with nonlinear dynamics of single neuron. Procedia IUTAM 22, 160–167 (2017)CrossRefGoogle Scholar
  6. 6.
    Azarfar, A., Calcini, N., Huang, C., Zeldenrust, F., Celikel, T.: Neural coding: a single neuron’s perspective. Neurosci. Biobehav. Rev. 94, 238–247 (2018)CrossRefGoogle Scholar
  7. 7.
    Fletcher, A.: Action potential: generation and propagation. Anaesth. Intensive Care Med. 17(4), 204–208 (2016)CrossRefGoogle Scholar
  8. 8.
    Ren, W., Hu, S.J., Zhang, B.J., Wang, F.Z., Gong, Y.F., Xu, J.: Period-adding bifurcation with chaos in the interspike intervals generated by an experimental neural pacemaker. Int. J. Bifurcat. Chaos 7(08), 1867–1872 (1997)CrossRefGoogle Scholar
  9. 9.
    Schoch, A., Pahle, J.: Requirements for band-pass activation of Ca2+-sensitive proteins such as NFAT. Biophys. Chem. 245, 41–52 (2019)CrossRefGoogle Scholar
  10. 10.
    Huang, S., Zhang, J., Wang, M., Hu, C.: Firing patterns transition and desynchronization induced by time delay in neural networks. Physica A 499, 88–97 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jia, B., Gu, H., Xue, L.: A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space. Cogn. Neurodyn. 11(2), 1–12 (2017)CrossRefGoogle Scholar
  12. 12.
    Bao, B.C., Wu, P.Y., Bao, H., Xu, Q., Chen, M.: Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator. Chaos. Soliton. Fract. 106, 161–170 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Shang, H., Xu, R., Wang, D., Zhou, J., Han, S.: A stochastic neural firing generated at a Hopf bifurcation and its biological relevance. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, E.S. (eds.) ICONIP 2017. LNCS, vol. 10637, pp. 553–562. Springer, Cham (2017). Scholar
  14. 14.
    Shang, H., et al.: Dynamical analysis of a stochastic neuron spiking activity in the biological experiment and its simulation by INa,P + I K model. In: Huang, T., Lv, J., Sun, C., Tuzikov, Alexander V. (eds.) ISNN 2018. LNCS, vol. 10878, pp. 850–859. Springer, Cham (2018). Scholar
  15. 15.
    Shang, H., Xu, R., Wang, D.: Dynamic analysis and simulation for two different chaos-like stochastic neural firing patterns observed in real biological system. In: Huang, D.-S., Bevilacqua, V., Premaratne, P., Gupta, P. (eds.) ICIC 2017. LNCS, vol. 10361, pp. 749–757. Springer, Cham (2017). Scholar
  16. 16.
    Shang, H., Jiang, Z., Xu, R., Wang, D., Wu, P., Chen, Y.: The dynamic mechanism of a novel stochastic neural firing pattern observed in a real biological system. Cogn. Syst. Res. 53, 123–136 (2019)CrossRefGoogle Scholar
  17. 17.
    Chay, T.R.: Chaos in a three-variable model of an excitable cell. Physica D 16(2), 233–242 (1985)CrossRefGoogle Scholar
  18. 18.
    Drukarch, B., et al.: Thinking about the nerve impulse: a critical analysis of the electricity-centered conception of nerve excitability. Prog. Neurobiol. 169, 172–185 (2018)CrossRefGoogle Scholar
  19. 19.
    Sun, W., Marongelli, E.N., Watkins, P.V., Barbour, D.L.: Decoding sound level in the marmoset primary auditory cortex. J. Neurophysiol. 118(4), 2024–2033 (2017)CrossRefGoogle Scholar
  20. 20.
    James, A., Karl, J., Michael, B.: Clinical applications of stochastic dynamic models of the brain, part I: a primer. Neurosci. Neuroimaging 2(3), 216–224 (2017)Google Scholar
  21. 21.
    Bakay, W.M.H., Anderson, L.A., Garcia-Lazaro, J.A., McAlpine, D., Schaette, R.: Hidden hearing loss selectively impairs neural adaptation to loud sound environments. Nat. Commun. 9(1), 4298 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Zhongting Jiang
    • 1
  • Dong Wang
    • 1
    • 2
    Email author
  • Jin Sun
    • 1
  • Hengyue Shi
    • 1
  • Huijie Shang
    • 1
  • Yuehui Chen
    • 1
    • 2
  1. 1.School of Information Science and EngineeringUniversity of JinanJinanChina
  2. 2.Key Laboratory of Medicinal Plant and Animal Resources of Qinghai-Tibet Plateau in Qinghai ProvinceQinghai Normal UniversityXiningChina

Personalised recommendations