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The photoreceptors can receive all kinds of visible light which is translated to the bioelectrical signal for the visual cortex. The function would be simulated by the photoelectric effect. This paper studies the dynamic characteristics of FitzHugh-Nagumo neurons coupled with a phototube. In the parameter space of phototube, the synchronization region of the coupled system in which the neuron mode is in chaos and burst, is discussed in detail; the data show that the forced resonance is prominent in the complete synchronization of the system when the coupling strength is low, while the phase synchronization is observed in numerical experiment when the coupling strength is strong. The active operation of the phototube, as well the inverse cutoff voltage can modulate the synchronization of the system. Our work can be used to understand the mechanism of the retinal diseases, such as macular degeneration.
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Keywords:
- neuron /
- phototube /
- synchronization /
- phase lock
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图 5 耦合系统中神经元的ISI和放电序列(f = 0.16) (a) ua = 0.1; (b) I0 = 1.5, ua = 0.1; (c) I0 = 2.5, ua = 0.1; (d) I0 = 0.3; (e) ua = 1.5, I0 = 0.3; (f) ua = 2.3, I0 = 0.3
Fig. 5. ISI and the firing sequence of neuron in the coupled system (f = 0.16): (a) ua = 0.1; (b) I0 = 1.5, ua = 0.1; (c) I0 = 2.5, ua = 0.1; (d) I0 = 0.3; (e) ua = 1.5, I0 = 0.3; (f) ua = 2.5, I0 = 0.3.
图 9 耦合系统中神经元的ISI和放电序列(f = 0.002) (a) ua = 0.01; (b) I0 = 0.5, ua = 0.01; (c) I0 = 1.5, ua = 0.01; (d) I0 = 0.3; (e) ua = 0.5, I0 = 0.3; (f) ua = 1.5, I0 = 0.3
Fig. 9. ISI and the firing sequence of neuron in the coupled system (f = 0.002): (a) ua = 0.01; (b) I0 = 0.5, ua = 0.1; (c) I0 = 1.5, ua = 0.1; (d) I0 = 0.3; (e) ua = 0.5, I0 = 0.3; (f) ua = 1.5, I0 = 0.3.
图 11 最大误差函数和最大相位差随参数的变化(灰色曲线为(6)式中的非线性耦合, 红色曲线为线性耦合) (a), (b) ua = 0.01; (c), (d) I0 = 0.001
Fig. 11. The maximum error function and the maximum phase difference change with the parameters, the grey curve represents the nonlinear coupling in Eq. (6) and the red curve is the linear one: (a), (b) ua = 0.01; (c), (d) I0 = 0.001.
图 12 系统误差、相位差和光电管功率随时间的演化(ua = 0.01) (a), (e), (i) I0 = 0.001; (b), (f), (j) I0 = 0.01; (c), (g), (k) I0 = 0.013; (d), (h), (l) I0 = 0.014
Fig. 12. Evolution of error function, phase error and phototube power (ua = 0.01): (a), (e), (i) I0 = 0.001; (b), (f), (j) I0 = 0.01; (c), (g), (k) I0 = 0.013; (d), (h), (l) I0 = 0.014.
表 1 不同外界刺激频率下的耦合FHN神经元分类
Table 1. Category of the coupled FHN neurons driven by external stimulation with different frequencies.
频率f 0.16 0.002 0.012 0.06 放电状态 混沌放电 簇放电 尖峰放电 周期放电 反向截止电压ua 0.1 0.5 0.01 0.5 0.01 0.5 0.01 0.5 耦合分类 case 1 case 2 case 3 case 4 case 5 case 6 case 7 case 8 -
[1] Ma J, Song X, Jin W, Wang C 2015 Chaos, Solitons Fractals 80 31
Google Scholar
[2] Iqbal M, Rehan M, Hong K S 2017 Plos One 12 e0176986
Google Scholar
[3] Sotero R C, Trujillo-Barreto N J 2008 Neuroimage 39 290
Google Scholar
[4] Izhikevich E M 2004 IEEE Trans. Neural Networks 15 1063
Google Scholar
[5] Ibarz B, Casado J M, Sanjuán M A F 2011 Phys. Rep. 501 1
Google Scholar
[6] Hodgkin A L, Huxley A F 1990 Bull. Math. Biol. 52 25
Google Scholar
[7] Fitzhugh R 1961 Biophys. J. 1 445
Google Scholar
[8] Shilnikov A 2012 Nonlinear Dyn. 68 305
Google Scholar
[9] Miesenbock G, Kevrekidis I G 2005 Annu. Rev. Neurosci. 28 533
Google Scholar
[10] Gu H, Pan B 2015 Nonlinear Dyn. 81 2107
Google Scholar
[11] Pikovskii A, Rabinovich M 1978 Dokl. Akad. Nauk SSSR 239 301
[12] Lv M, Wang C, Ren G, Ma J, Song X 2016 Nonlinear Dyn. 85 1479
Google Scholar
[13] Baines P G 2008 Prog. Phys. Geogr. 32 475
Google Scholar
[14] Zhang X, Wang C, Ma J, Ren G 2020 Mod. Phys. Lett. B 2050267
Google Scholar
[15] Zhang G, Ma J, Alsaedi A, Ahmad B, Alzahrani F 2018 Appl. Math. Comput. 321 290
Google Scholar
[16] Yao Z, Ma J, Yao Y, Wang C 2019 Nonlinear Dyn. 96 205
Google Scholar
[17] Xu Y M, Yao Z, Hobiny A, Ma J 2019 Front. Inform. Tech. El. 20 571
Google Scholar
[18] Liu Z, Wang C, Jin W, Ma J 2019 Nonlinear Dyn. 97 2661
Google Scholar
[19] Tosini G, Doyle S, Geusz M, Menaker M 2000 Proc. Natl. Acad. Sci. 97 11540
Google Scholar
[20] Menaker M 1972 Sci. Am. 226 22
Google Scholar
[21] Kennedy D 1958 Am. J. Ophthal. 46 19
Google Scholar
[22] Martenson M E, Halawa O I, Tonsfeldt K J, et al. 2016 Pain 157 868
Google Scholar
[23] Liu Y, Xu W J, Ma J, Alzahrani F, Hobiny A 2020 Front. Inform. Tech. El. 21 1387
Google Scholar
[24] Li J R, Wang J P, Jiang L 1994 Biosens. Bioelectron. 9 147
Google Scholar
[25] Zou W, Senthilkumar D V, Zhan M, Kurths J 2013 Phys. Rev. Lett. 111 014101
Google Scholar
[26] Wu Y, Xiao J, Hu G, Zhan M 2012 EPL 97 40005
Google Scholar
[27] Perc M 2009 Biophys. Chem. 141 175
Google Scholar
[28] Lin W, Wang Y, Ying H, Lai Y C, Wang X 2015 Phys. Rev. E 92 012912
Google Scholar
[29] 张平伟, 唐国宁, 罗晓曙 2005 物理学报 54 3497
Google Scholar
Zhang P W, Tang G N, Luo X S 2005 Acta Phys. Sin. 54 3497
Google Scholar
[30] Wouapi K M, Fotsin B H, Louodop F P, Feudjio K F, Njitacke Z T, Djeudjo T H 2020 Cogn. Neurodyn. 14 375
Google Scholar
[31] Shafiei M, Jafari S, Parastesh F, Ozer M, Kapitaniak T, Perc M 2020 Commun. Nonlinear Sci. Numer. Simul. 84 105175
Google Scholar
[32] Phan C, You Y 2020 Nonlinear. Anal.-Real 55 103139
Google Scholar
[33] Moayeri M M, Rad J A, Parand K 2020 Comput. Math. Appl. 80 1887
Google Scholar
[34] Makovkin S Y, Shkerin I V, Gordleeva S Y, Ivanchenko M V 2020 Chaos, Solitons Fractals 138 109951
Google Scholar
[35] Zou Y L, Zhu J, Chen G, Luo X S 2005 Chaos, Solitons Fractals 25 1245
Google Scholar
[36] Zhou S, Hong Y, Yang Y, Lü L, Li C 2020 Pramana J. Phys. 94 34
Google Scholar
[37] Venkatesh P, Venkatesan A, Lakshmanan M 2016 Pramana J. Phys. 86 1195
Google Scholar
[38] Sivaganesh G, Sweetlin M D, Arulgnanam A 2016 J. Korean Phys. Soc. 69 124
Google Scholar
[39] Binczak S, Jacquir S, Bilbault J M, Kazantsev V B, Nekorkin V I 2006 Neural Networks 19 684
Google Scholar
[40] Wade J J, Mcdaid L J, Harkin J, Crunelli V, Kelso J S 2011 PloS One 6 e29445
Google Scholar
[41] Sambas A, WS M S, Mamat M 2015 J. Eng. Sci. Tech. Rev. 8 89
Google Scholar
[42] Daoudal G, Hanada Y, Debanne D 2002 PNAS 99 14512
Google Scholar
[43] Chorev E, Brecht M 2012 J. Neurophysiol. 108 1584
Google Scholar
[44] 杨永霞, 李玉叶, 古光华 2020 物理学报 69 040501
Google Scholar
Yhang Y X, Li Y Y, Gu G H 2020 Acta Phys. Sin. 69 040501
Google Scholar
[45] 汪芃, 李倩昀, 唐国宁 2018 物理学报 67 030502
Google Scholar
Wang P, Li Q Y, Tang G N 2018 Acta Phys. Sin. 67 030502
Google Scholar
[46] FitzHugh R 1955 Bull. Math. Biophys. 17 257
Google Scholar
[47] Nagumo J, Arimoto S, Yoshizawa S 1962 Proc. IRE 50 2061
Google Scholar
[48] Kawato M, Suzuki R 1980 J. Theor. Biol. 86 547
Google Scholar
[49] Okuda M 1981 Prog. Theor. Phys. 66 90
Google Scholar
[50] Treutlein H, Schulten K 1985 Ber. Bunse. Ges. Phys. Chem. 89 710
Google Scholar
[51] Rajasekar S, Lakshmanan M 1988 J. Theor. Biol. 133 473
Google Scholar
[52] Einstein A 1905 Ann. Physik. 17 132
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