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Stochastic resonance (SR) is studied in the FitzHugh-Nagumo (FHN) neural system subject to multiplicative non-Gaussian noise, additive Gaussian white noise and a periodic signal. Using the path integral approach and the two-state theory, the expression of the signal-to-noise ratio (SNR) is derived. The simulation results show that conventional SR and double SR occur in the FHN neural model under different values of system parameters. The effects of the additive and multiplicative noise intensities on SNR are different. Moreover, the addition of non-Gaussian noise is conductive to the enhancement of the response to the output signal of the FHN neural system.
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Keywords:
- non-Gaussian noise /
- FHN neural system /
- stochastic resonance
[1] Hodgkin A L, Huxley A F 1952 J. Gen. Physiol 117 500
[2] FitzhHugh R 1960 J. Gen. Physiol 43 867
[3] Alarcon T, Perez-Madrod A, Rubi J M 1998 Phys. Rev. E 57 4979
[4] Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[5] Nozaki D, Mar D J, Grigg P, Coliins J J 1999 Phys. Rev. Lett. 82 2402
[6] Zhang G J, Xu J X 2005 Chaos, Solitons & Fractals 23 1439
[7] Wang Q Y, Shi X, Lu Q S 2008 Synchronization Dynamics in the Coupled System of Neurons (Beijing: Science Press) (in Chinese) [王青云, 石霞, 陆启韶 2008 神经元耦合系统的同步动力学(北京: 科学出版社)]
[8] Wang Q Y, Lu Q S, Chen G R, Feng Z S, Duan L X 2009 Chaos, Solitons & Fractals 39 918
[9] Zhen B, Xu J 2010 Commun Nonlinear Sci. Numer. Simulat. 15 442
[10] Fan D J, Hong L 2010 Commun Nonlinear Sci. Numer. Simulat. 15 1873
[11] Wang C Q, Xu W, Zhang N M, Li H Q 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆, 徐伟, 张娜敏, 李海泉 2008 57 749]
[12] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇, 谢勇 2010 59 2147]
[13] Yu S N, Jia Y 2000 Journal of Central China Normal University (Nat. Sci.) 34 281
[14] Zeng C H, Zeng C P, Gong A L, Nie L R 2010 Physica A 389 5117
[15] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 59 3727]
[16] Bezrukov S M, Vodyanoy I 1997 Nature 385 319
[17] Goychuk I, Hänggi P 2000 Phys. Rev. E 61 4272
[18] Fuentes M A, Toral R, Wio H S 2001 Physica A 295 114
[19] Fuentes M A, Wio H S, Toral R 2002 Physica A 303 91
[20] Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
[21] Gu R C, Xu Y, Zhang H Q, Sun Z K 2011 Acta Phys. Sin. 60 110514 (in Chinese) [顾仁财, 许勇, 张慧清, 孙中奎 2011 60 110514]
[22] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
[23] Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵燕, 徐伟, 邹少存 2009 58 1396]
[24] Xu C, Kang Y M 2011 Acta Phys. Sin. 60 108701 (in Chinese) [徐超, 康艳梅 2011 60 108701]
[25] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡岗 1994 随机力与非线性系统 (上海: 上海科技教育出版社)]
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[1] Hodgkin A L, Huxley A F 1952 J. Gen. Physiol 117 500
[2] FitzhHugh R 1960 J. Gen. Physiol 43 867
[3] Alarcon T, Perez-Madrod A, Rubi J M 1998 Phys. Rev. E 57 4979
[4] Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[5] Nozaki D, Mar D J, Grigg P, Coliins J J 1999 Phys. Rev. Lett. 82 2402
[6] Zhang G J, Xu J X 2005 Chaos, Solitons & Fractals 23 1439
[7] Wang Q Y, Shi X, Lu Q S 2008 Synchronization Dynamics in the Coupled System of Neurons (Beijing: Science Press) (in Chinese) [王青云, 石霞, 陆启韶 2008 神经元耦合系统的同步动力学(北京: 科学出版社)]
[8] Wang Q Y, Lu Q S, Chen G R, Feng Z S, Duan L X 2009 Chaos, Solitons & Fractals 39 918
[9] Zhen B, Xu J 2010 Commun Nonlinear Sci. Numer. Simulat. 15 442
[10] Fan D J, Hong L 2010 Commun Nonlinear Sci. Numer. Simulat. 15 1873
[11] Wang C Q, Xu W, Zhang N M, Li H Q 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆, 徐伟, 张娜敏, 李海泉 2008 57 749]
[12] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇, 谢勇 2010 59 2147]
[13] Yu S N, Jia Y 2000 Journal of Central China Normal University (Nat. Sci.) 34 281
[14] Zeng C H, Zeng C P, Gong A L, Nie L R 2010 Physica A 389 5117
[15] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 59 3727]
[16] Bezrukov S M, Vodyanoy I 1997 Nature 385 319
[17] Goychuk I, Hänggi P 2000 Phys. Rev. E 61 4272
[18] Fuentes M A, Toral R, Wio H S 2001 Physica A 295 114
[19] Fuentes M A, Wio H S, Toral R 2002 Physica A 303 91
[20] Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
[21] Gu R C, Xu Y, Zhang H Q, Sun Z K 2011 Acta Phys. Sin. 60 110514 (in Chinese) [顾仁财, 许勇, 张慧清, 孙中奎 2011 60 110514]
[22] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
[23] Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵燕, 徐伟, 邹少存 2009 58 1396]
[24] Xu C, Kang Y M 2011 Acta Phys. Sin. 60 108701 (in Chinese) [徐超, 康艳梅 2011 60 108701]
[25] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡岗 1994 随机力与非线性系统 (上海: 上海科技教育出版社)]
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