Abstract
In this study, the deterministic Chay model is improved considering the K+ channel opening probability during the generation of the generation mechanism of action potential. It can not only simulate the periodic firing, chaos and periodic-adding bifurcation that the original Chay model can simulate, but also simulate the rhythm that the original model cannot simulate, which enhances the simulation ability of the model. The simulation results show that the unification of certainty and randomness in the deterministic system for the first time.
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References
Atencio, C.A., Sharpee, T.O., Schreiner, C.E.: Cooperative nonlinearities in auditory cortical neurons. Neuron 58(6), 956–966 (2008)
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)
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)
Yang, Y., Solis-Escalante, T., van der Helm, F., Schouten, A.: A generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system. IEEE Trans. Biomed. Eng. 25(4), 401–410 (2008)
Zhao, Z., Gu, H.: Identifying time delay-induced multiple synchronous behaviours in inhibitory coupled bursting neurons with nonlinear dynamics of single neuron. Proc. IUTAM 22, 160–167 (2017)
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)
Yang, M., An, S., Gu, H., Liu, Z., Ren, W.: Understanding of physiological neural firing patterns through dynamical bifurcation machineries. NeuroReport 17(10), 995–999 (2006)
Huang, S., Zhang, J., Wang, M., Hu, C.: Firing patterns transition and desynchronization induced by time delay in neural networks. Phys. A 499, 88–97 (2018)
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)
Jia, B., Gu, H.: Dynamics and physiological roles of stochastic firing patterns near bifurcation points. Int. J. Bifurcat. Chaos. 27(7), 1750113 (2017)
Evans-Martin, F.F.: The Nervous System. Infobase Publishing (2009)
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)
Gu, H., Zhang, H., Wei, C., Yang, M., Liu, Z., Ren, W.: Coherence resonance–induced stochastic neural firing at a saddle-node bifurcation. Int. J. Mod. Phys. B 25(29), 3977–3986 (2011)
Li, D., Hu, B., Wang, J., Jing, Y., Hou, F.: Coherence resonance in the two-dimensional neural map driven by non-Gaussian colored noise. Int. J. Mod. Phys. B 30(5), 1650012 (2016)
Liu, J., Mao, J., Huang, B., Liu, P.: Chaos and reverse transitions in stochastic resonance. Phys. Lett. A 382(42), 3071–3078 (2018)
Shaw, P.K., Chaubey, N., Mukherjee, S., Janaki, M.S., Iyengar, A.N.: A continuous transition from chaotic bursting to chaotic spiking in a glow discharge plasma and its associated long range correlation to anti correlation behaviour. Phys. A 513, 126–134 (2019)
Zlatkovic, B.M., Samardzic, B.: Multiple spatial limit sets and chaos analysis in MIMO cascade nonlinear systems. Chaos. Soliton. Fract. 119, 86–93 (2019)
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: International Conference on Intelligent Computing, pp. 749–757 (2017)
Chay, T.R.: Chaos in a three-variable model of an excitable cell. Phys. D 16(2), 233–242 (1985)
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)
Acknowledgment
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), the Youth Science and Technology Star Program of Jinan City (201406003), the Nature Science Research Fund of Jiangsu Province of China (No. BK20161165), and the applied fundamental research Foundation of Xuzhou of China (No. KC17072).
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Jiang, Z., Wang, D., Shang, H., Chen, Y. (2019). Simulation of Complex Neural Firing Patterns Based on Improved Deterministic Chay Model. In: Huang, DS., Jo, KH., Huang, ZK. (eds) Intelligent Computing Theories and Application. ICIC 2019. Lecture Notes in Computer Science(), vol 11644. Springer, Cham. https://doi.org/10.1007/978-3-030-26969-2_15
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DOI: https://doi.org/10.1007/978-3-030-26969-2_15
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