Synchronization between FitzHugh-Nagumo neurons coupled with phototube

Zhang Xiu-Fang; Ma Jun; Xu Ying; Ren Guo-Dong

doi:10.7498/aps.70.20201953

Abstract

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.

Keywords:

Authors and contacts

1.
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
2.
School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China

Corresponding author: Ren Guo-Dong, rengd@lut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11672122, 12062009) and the Natural Science Foundation of Gansu Province, China (Grant No. 20JR5RA473)

FullText HTML : translate this paragraph

References

[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

Cited By

图 1 FHN神经元的等效电路图

Figure 1. Equivalent circuit diagram of FHN neuron.

DownLoad: Full-Size Img PowerPoint

图 2 光电管的电流-电压特性

Figure 2. I-V characteristics of phototube.

DownLoad: Full-Size Img PowerPoint

图 3 光电管耦合FHN神经元系统的等效电路图

Figure 3. Equivalent circuit diagram of the coupled FHN neuron system.

DownLoad: Full-Size Img PowerPoint

图 4 单个FHN神经元在不同参数下的ISI　(a) b = 0.8, c = 0.1; (b) a = 0.7, c = 0.1; (c) a = 0.7, b = 0.8

Figure 4. ISI of single FHN neuron with different parameters: (a) b = 0.8, c = 0.1; (b) a = 0.7, c = 0.1; (c) a = 0.7, b = 0.8.

DownLoad: Full-Size Img PowerPoint

图 5 耦合系统中神经元的ISI和放电序列(f = 0.16)　(a) u_a = 0.1; (b) I₀ = 1.5, u_a = 0.1; (c) I₀ = 2.5, u_a = 0.1; (d) I₀ = 0.3; (e) u_a = 1.5, I₀ = 0.3; (f) u_a = 2.3, I₀ = 0.3

Figure 5. ISI and the firing sequence of neuron in the coupled system (f = 0.16): (a) u_a = 0.1; (b) I₀ = 1.5, u_a = 0.1; (c) I₀ = 2.5, u_a = 0.1; (d) I₀ = 0.3; (e) u_a = 1.5, I₀ = 0.3; (f) u_a = 2.5, I₀ = 0.3.

DownLoad: Full-Size Img PowerPoint

图 6 u_a和I₀的参数空间中, 耦合系统(case 1)的同步区间　(a)最大误差函数θ_max; (b)最大相位差∆ϕ_max

Figure 6. Synchronization region of the coupled system (case 1) in the parameter space of u_a vs. I₀: (a) Maximum error function θ_max; (b) maximum phase difference ∆ϕ_max.

DownLoad: Full-Size Img PowerPoint

图 7 误差函数、相位差和功率随时间的演化(u_a = 0.1)　(a), (e), (i) I₀ = 0.01; (b), (f), (j) I₀ = 0.2; (c), (g), (k) I₀ = 0.8; (d), (h), (l) I₀ = 1

Figure 7. Evolution of error function, phase difference and power (u_a = 0.1): (a), (e), (i) I₀ = 0.01; (b), (f), (j) I₀ = 0.2; (c), (g), (k) I₀ = 0.8; (d), (h), (l) I₀ = 1.

DownLoad: Full-Size Img PowerPoint

图 8 系统误差与相位差随时间的演化(u_a = 0.5)　(a), (e) I₀ = 0.01; (b), (f) I₀ = 0.2; (c), (g) I₀ = 0.8; (d), (h) I₀ = 1

Figure 8. Evolution of error function and phase error (u_a = 0.5): (a), (e) I₀ = 0.01; (b), (f) I₀ = 0.2; (c), (g) I₀ = 0.8; (d), (h) I₀ = 1.

DownLoad: Full-Size Img PowerPoint

图 9 耦合系统中神经元的ISI和放电序列(f = 0.002)　(a) u_a = 0.01; (b) I₀ = 0.5, u_a = 0.01; (c) I₀ = 1.5, u_a = 0.01; (d) I₀ = 0.3; (e) u_a = 0.5, I₀ = 0.3; (f) u_a = 1.5, I₀ = 0.3

Figure 9. ISI and the firing sequence of neuron in the coupled system (f = 0.002): (a) u_a = 0.01; (b) I₀ = 0.5, u_a = 0.1; (c) I₀ = 1.5, u_a = 0.1; (d) I₀ = 0.3; (e) u_a = 0.5, I₀ = 0.3; (f) u_a = 1.5, I₀ = 0.3.

DownLoad: Full-Size Img PowerPoint

图 10 u_a和I₀的参数空间中, 耦合系统(case 3)的同步区间　(a)最大误差函数θ_max; (b)最大相位差∆ϕ_max

Figure 10. Synchronization region of the coupled system (case 3) in the parameter space of u_a vs. I₀: (a) Maximum error function θ_max; (b) maximum phase difference ∆ϕ_max.

DownLoad: Full-Size Img PowerPoint

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) u_a = 0.01; (c), (d) I₀ = 0.001

Figure 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) u_a = 0.01; (c), (d) I₀ = 0.001.

DownLoad: Full-Size Img PowerPoint

图 12 系统误差、相位差和光电管功率随时间的演化(u_a = 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

Figure 12. Evolution of error function, phase error and phototube power (u_a = 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.

DownLoad: Full-Size Img PowerPoint

图 13 系统误差与相位差随时间的演化(u_a = 0.5)　(a), (e) I₀ = 0.001; (b), (f) I₀ = 0.01; (c), (g) I₀ = 0.013; (d), (h) I₀ = 0.014

Figure 13. Evolution of error function and phase error for variables (u_a = 0.5): (a), (e) I₀ = 0.001; (b), (f) I₀ = 0.01; (c), (g) I₀ = 0.013; (d), (h) I₀ = 0.014.

DownLoad: Full-Size Img PowerPoint

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u_a 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

DownLoad: CSV

[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

[1]	Ma Shao-Qing, Gong Shi-Xiang, Zhang Wei, Lu Cheng-Biao, Li Xiao-Li, Li Ying-Wei. Neuronal growth and development promoted by low-intensity roadband terahertz radiation. Acta Physica Sinica, 2022, 71(20): 208701. doi: 10.7498/aps.71.20220636
[2]	Bai Jing, Guan Fu-Rong, Tang Guo-Ning. Various effects induced by local synchronization in neural networks. Acta Physica Sinica, 2021, 70(17): 170502. doi: 10.7498/aps.70.20210142
[3]	Xie Ying, Zhu Zhi-Gang, Zhang Xiao-Feng, Ren Guo-Dong. Control of firing mode in nonlinear neuron circuit driven by photocurrent. Acta Physica Sinica, 2021, 70(21): 210502. doi: 10.7498/aps.70.20210676
[4]	Wei Tian-Li, Wu De-Wei, Yang Chun-Yan, Luo Jun-Wen, Miao Qiang, Li Xiang. A phase locking scheme of two-mode squeezed microwave preparation. Acta Physica Sinica, 2020, 69(3): 034204. doi: 10.7498/aps.69.20191348
[5]	Yu Wen-Ting, Zhang Juan, Tang Jun. Effects of dynamic synapses, neuronal coupling, and time delay on firing of neuron. Acta Physica Sinica, 2017, 66(20): 200201. doi: 10.7498/aps.66.200201
[6]	Xiu Chun-Bo, Liu Chang, Guo Fu-Hui, Cheng Yi, Luo Jing. Control strategy and application of hysteretic chaotic neuron and neural network. Acta Physica Sinica, 2015, 64(6): 060504. doi: 10.7498/aps.64.060504
[7]	Wang Fu-Xia, Xie Yong. Synchronization of "Hopf/homoclinic" bursting with "SubHopf/homoclinic" bursting. Acta Physica Sinica, 2013, 62(2): 020509. doi: 10.7498/aps.62.020509
[8]	Wu Wang-Sheng, Tang Guo-Ning. Synchronizations of chaotic neuronal networks under different couplings. Acta Physica Sinica, 2012, 61(7): 070505. doi: 10.7498/aps.61.070505
[9]	Wang Xing-Yuan, Ren Xiao-Li, Zhang Yong-Lei. Full-order and reduced-order optimal synchronization of neurons model with unknown parameters. Acta Physica Sinica, 2012, 61(6): 060508. doi: 10.7498/aps.61.060508
[10]	Li Chun-Guang, Chen Jun. Circuit design of tabu learning neuron models and their dynamic behavior. Acta Physica Sinica, 2011, 60(2): 020502. doi: 10.7498/aps.60.020502
[11]	Wang Zheng, Zhao Xin-Jie, He Ming, Zhou Tie-Ge, Yue Hong-Wei, Yan Shao-Lin. Simulations of impedance matching and phase locking of Josephson junction arrays embedded in a Fabry-Perot resonator. Acta Physica Sinica, 2010, 59(5): 3481-3487. doi: 10.7498/aps.59.3481
[12]	He Guo-Guang, Zhu Ping, Chen Hong-Ping, Xie Xiao-Ping. Synchronization in a threshold coupled chaotic neuronal map. Acta Physica Sinica, 2010, 59(8): 5307-5312. doi: 10.7498/aps.59.5307
[13]	Liu Yong, Xie Yong. Dynamical characteristics of the fractional-order FitzHugh-Nagumo model neuron and its synchronization. Acta Physica Sinica, 2010, 59(3): 2147-2155. doi: 10.7498/aps.59.2147
[14]	Wang Hui-Qiao, Yu Lian-Chun, Chen Yong. Effects of channel noise on metabolic energy cost of action potentials. Acta Physica Sinica, 2009, 58(7): 5070-5074. doi: 10.7498/aps.58.5070
[15]	Qiao Xiao-Yan, Li Gang, Dong You-Er, He Bing-Jun. Neuron excitability changes induced by low-power laser irradiation. Acta Physica Sinica, 2008, 57(2): 1259-1265. doi: 10.7498/aps.57.1259
[16]	Lei Bing, Feng Ying, Liu Ze-Jin. Phase locking of three fiber lasers using an all-fiber coupling loop. Acta Physica Sinica, 2008, 57(10): 6419-6424. doi: 10.7498/aps.57.6419
[17]	Qiao Xiao-Yan, Li Gang, Lin Ling, He Bing-Jun. Research on characteristics of neuron potassium channel under low level laser irradiation. Acta Physica Sinica, 2007, 56(4): 2448-2455. doi: 10.7498/aps.56.2448
[18]	Wang Zhan-Shan, Zhang Hua-Guang, Wang Zhi-Liang. Global synchronization of a class of chaotic neural networks. Acta Physica Sinica, 2006, 55(6): 2687-2693. doi: 10.7498/aps.55.2687
[19]	Yan Sen-Lin. Studies on chaotic multiple-quantum-well laser synchronization via controlling phase and its application in secure communication using external chaos phase shift keying modulation. Acta Physica Sinica, 2005, 54(3): 1098-1104. doi: 10.7498/aps.54.1098
[20]	Wu Ying, Xu Jian-Xue, He Dai-Hai, Jin Wu-Yin. Study on nonlinear characteristics of two synchronizing uncoupled Hindmarsh-Rose neurons. Acta Physica Sinica, 2005, 54(7): 3457-3464. doi: 10.7498/aps.54.3457

Catalog

Vol. 70, Issue 9 - 2021-05-05

Metrics

Abstract views: 5950
PDF Downloads: 139
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板