电磁感应下一类新皮层神经元的放电及同步

doi:10.6040/j.issn.1671-9352.0.2020.712

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (5): 1-11.doi: 10.6040/j.issn.1671-9352.0.2020.712

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电磁感应下一类新皮层神经元的放电及同步

祁慧敏¹,张莉²,安新磊^1*,乔帅¹,肖冉¹

1.兰州交通大学数理学院, 甘肃兰州 730070;2.兰州工业学院基础学科部, 甘肃兰州 730050

发布日期:2021-05-13
作者简介:祁慧敏(1995— ),女,硕士研究生,研究方向为非线性动力学. E-mail:597701222@qq.com *通信作者简介:安新磊(1983— ),男,博士,教授,研究方向为非线性动力学. E-mail:anxin1983@163.com
基金资助:
国家自然科学基金资助项目(119620112)

Firing and synchronization of a neocortical neuron under electromagnetic induction

QI Hui-min¹, ZHANG Li², AN Xin-lei^1*, QIAO Shuai¹, XIAO Ran¹

1.School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China;
2.Department of Basic Science, Lanzhou Institute of Technology, Lanzhou 730050, Gansu, China

Published:2021-05-13

摘要/Abstract

摘要： 通过引入磁通变量实现电磁感应电流对膜电位的调制,建立一类新皮层神经元的四维神经元模型。基于单参数分岔图、双参数分岔图及其相应的最大李雅普诺夫指数图详细地分析该模型的放电特性和分岔模式。数值结果表明,该模型在适当的外界刺激和电磁感应强度作用下会产生复杂的分岔行为,即加周期分岔、倍周期和逆倍周期分岔等。有趣的是,该模型在双参数平面上广泛存在“梳”状的混沌结构,这意味着该模型具有含混沌的加周期分岔模式。同时基于李雅普诺夫稳定性理论证实了该模型在适当的磁通耦合强度下可以达到完全同步,在较强的耦合条件下反而会破坏同步行为。

关键词: 电磁耦合, 新皮层神经元, 分岔分析, 最大李雅普诺夫指数, 完全同步

Abstract: A four-dimensional neuron model of a class of neocortical neurons is established by introducing the flux variable to modulate the membrane potential of the electromagnetic induced current. Based on single parameter bifurcation diagram, the double parameter bifurcation diagram and the corresponding maximum Lyapunov exponent diagram analysis of the discharge characteristics of the model in detail and bifurcation model, the numerical results show that the model in the appropriate external stimuli and under the action of electromagnetic induction intensity will produce complex bifurcation behaviors, namely periodic bifurcation and period-doubling and inverse period-doubling bifurcation, etc. Interestingly, the model has a “comb-shaped” chaotic structure in a two-parameter plane, which means that the model has a period-added bifurcation model with chaos. Meanwhile, based on Lyapunov stability theory, it is proved that the model can achieve complete synchronization under appropriate flux coupling strength, but will destroy the synchronization behavior under strong coupling condition.

Key words: electromagnetic coupling, neocortical neurons, bifurcation analysis, maximum Lyapunov exponent, complete synchronization

中图分类号:

O441.3

祁慧敏,张莉,安新磊,乔帅,肖冉. 电磁感应下一类新皮层神经元的放电及同步[J]. 《山东大学学报(理学版)》, 2021, 56(5): 1-11.

QI Hui-min, ZHANG Li, AN Xin-lei, QIAO Shuai, XIAO Ran. Firing and synchronization of a neocortical neuron under electromagnetic induction[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(5): 1-11.

参考文献

[1] BRAUN H A, WISSING H, SCHAFER K, et al. Oscillation and noise determine signal transduction in shark multimodal sensory cells[J]. Nature, 1994, 367(6460):270-273.
[2] YANG Minghao, AN Shucheng, GU Huaguang, et al. Understanding of physiological neural firing patterns through dynamical bifurcation machineries[J]. Neuroreport, 2006, 17(10):995-999.
[3] PEDARZANI P, MOSBACHER J, RIVARD A, et al. Control of electrical activity in central neurons by modulating the gating of small conductance cc+-activated K+channels[J]. Journal of Biological Chemistry, 2001, 276(13):9762-9769.
[4] HODGKIN A L, HUXLEY A F. The components of membrane conductance in the giant axon of Loligo[J]. The Journal of physiology, 1952, 116(4):473-496.
[5] IZHIKEVICH E M. Dynamical systems in neuroscience: the geometry of excitability and bursting[M]. Boston: Massachusetts Institute of Technology Press, 2007.
[6] HINDMARSH J L, ROSE R M. A model of neuronal bursting using three coupled first order differential equations[J]. Proceedings of the Royal Society B: Biological Sciences, 1984, 221(1222):87-102.
[7] QIAO Shuai, AN Xinlei. Dynamic expression of a HR neuron model under an electric field[J]. International Journal of Modern Physics B, 2021, 35(2): 2150024.
[8] WU Fuqiang, WANG Chunni, JIN Wuyin, et al. Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise[J]. Physica A: Statal Mechanics and its Applications, 2017, 469(1):81-88.
[9] BAO Hao, ZHU Dong, LIU Wenbo, et al. Memristor synapse-based Morris-Lecar model: bifurcation analyses and FPGA-based validations for periodic and chaotic bursting/spiking firings[J]. International Journal of Bifurcation and Chaos, 2020, 30(3):2050045.
[10] 安新磊, 张莉.一类忆阻神经元的电活动多模振荡及Hamilton能量反馈控制[J].力学学报,2020, 52(4):1174-1188. AN Xinlei, ZHANG Li. Multimode oscillation of electrical activity and Hamilton energy feedback control of a class of membrance neurons[J]. Chinese Journal of Mechanics, 2020, 52(4):1174-1188.
[11] 乔帅,安新磊,王红梅, 等.电磁感应下HR神经元模型的分岔分析与控制[J].山东大学学报(理学版), 2020, 55(9):1-9. QIAO Shuai, AN Xinlei, WANG Hongmei, et al. Bifurcation analysis and control of HR neuron model under electromagnetic induction[J]. Journal of Shandong University(Natural Science), 2020, 55(9):1-9.
[12] LV Mi, MA Jun. Multiple modes of electrical activities in a new neuron model under electromagnetic radiation[J]. Neurocomputing, 2016, 205(12):375-381.
[13] YAN Bo, PANAHI S, HE Shaobo, et al. Further dynamical analysis of modified Fitzhugh-Nagumo model under the electric field[J]. Nonlinear Dynamics, 2020, 101:521-529.
[14] LIU Ying, MA Jun, XU Ying, et al. Electrical mode transition of hybrid neuronal model induced by external stimulus and electromagnetic induction[J]. International Journal of Bifurcation and Chaos, 2019, 29(11):1950156.
[15] LV Mi, WANG Chunni, REN Guodong, et al. Model of electrical activity in a neuron under magnetic flow effect[J]. Nonlinear Dynamics, 2016, 85(3):1479-1490.
[16] MA J, ZHANG G, HAYAT T, et al. Model electrical activity of neuron under electric field[J]. Nonlinear Dynamics, 2019, 95(2):1585-1598.
[17] 王海侠, 陆启韶.神经元耦合系统同步条件的几点注记[J].北京航空航天大学学报, 2006, 32(3):320-323. WANG Haixia, LU Qishao. Several notes on synchronization conditions of neuron-coupled systems[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(3):320-323.
[18] ZHAO X, KIM J W, ROBINSON P A, et al. Low dimensional model of bursting neurons[J]. Journal of Computational Neuroscience, 2014, 36(1):81-95.
[19] FAN Denggui, WANG Qingyun. Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays[J]. Science China Technological Science, 2017, 60(7):1019-1031.
[20] 李强.Maple 8基础应用教程[M].北京:中国水利水电出版社, 2004. LI Qiang.Maple 8 basic application course[M]. Beijing: China Water Resources and Hydropower Press, 2004.

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电磁感应下一类新皮层神经元的放电及同步

Firing and synchronization of a neocortical neuron under electromagnetic induction

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