Simulation of a Chaos-Like Irregular Neural Firing Pattern Based on Improved Deterministic Chay Model
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.
KeywordsNeural 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).
- 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). https://doi.org/10.1007/978-3-319-70093-9_58CrossRefGoogle Scholar
- 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). https://doi.org/10.1007/978-3-319-92537-0_96CrossRefGoogle Scholar
- 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). https://doi.org/10.1007/978-3-319-63309-1_66CrossRefGoogle Scholar
- 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