摘要The vibrational resonance and stochastic resonance phenomena in the FitzHugh–Nagumo (FHN) neural model, driven by a high-frequency (HF) signal and a low-frequency (LF) signal and by coupled multiplicative and additive noises, is investigated. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with the increasing intensities of the multiplicative and additive noise as well as with the increasing system parameters of the FHN model. The influence of the coupling strength between the multiplicative and additive noises on the SNR is discussed.
Abstract：The vibrational resonance and stochastic resonance phenomena in the FitzHugh–Nagumo (FHN) neural model, driven by a high-frequency (HF) signal and a low-frequency (LF) signal and by coupled multiplicative and additive noises, is investigated. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with the increasing intensities of the multiplicative and additive noise as well as with the increasing system parameters of the FHN model. The influence of the coupling strength between the multiplicative and additive noises on the SNR is discussed.
(Probability theory, stochastic processes, and statistics)
引用本文:
HE Zheng-You;ZHOU Yu-Rong**
. Vibrational and Stochastic Resonance in the FitzHugh–Nagumo Neural Model with Multiplicative and Additive Noise[J]. 中国物理快报, 2011, 28(11): 110505-110505.
HE Zheng-You, ZHOU Yu-Rong**
. Vibrational and Stochastic Resonance in the FitzHugh–Nagumo Neural Model with Multiplicative and Additive Noise. Chin. Phys. Lett., 2011, 28(11): 110505-110505.
[1] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A: Math Gen. 14 L453
[2] Gammaitoni L, Hänggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3] Guo F, Zhou Y R and Zhang Y 2010 Chin. Phys. Lett. 27 090506
[4] Zhou Y R 2010 Chin. Phys. Lett. 27 080502
[5] Landa P S and McClintock P V E 2000 J. Phys A: Math. Gen. 33 L433
[6] Maksimov A 1997 Ultrasonics 35 79
[7] Jin Y F, Xu W and Xu M 2005 Chin. Phys. Lett. 22 1061
[8] Baltanas J P, Lopez L, Blechman I I, Landa P S, Zaikin A, Kurths J and Sanjuan M A F 2003 Phys. Rev. E 67 066119
[9] Jeyakumari S, Chinnathambi V, Rajasekar S and Sanjuan M A F 2009 Phys. Rev. E 80 046608
[10] Chizhevsky V N and Giacomelli G 2005 Phys. Rev. A 71 011801(R)
[11] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[12] Bonhoefer K F 1948 J. Gen. Physiol. 32 69
[13] Treutlein H, Schulten K and Bunsenges B 1985 Phys. Chem. 89 710
[14] Shinohara Y, Kanamaru T, Suzuki H, Horita T and Aihara K 2002 Phys. Rev. E 65 051906
[15] Pankratov E V, Polovinkin A V and Spagnolo B 2005 Phys. Lett. A 344 43
[16] Tessonea C J and Wio H S 2007 Physica A 374 46
[17] Cubero D, Baltanás J P and CasadoPascual J 2006 Phys. Rev. E 73 061102
[18] Fulinski A and Telejko T 1991 Phys. Lett. A 152 11
[19] Zeng C H, Zeng C P, Gong A L and Nie L R 2010 Physica A 389 5117
[20] Lindner B and SchimanskyGeier L 1999 Phys. Rev. E 60 7270
[21] McNamara B and Wiesenfeld K 1989 Phys. Rev . A 39 4854
[22] Bouzat S and Wio H S 1999 Phys. Rev. E 59 5142
[23] Wio H S and Bouzat S 1999 Braz. J. Phys. 29 136
[24] Hanggi P, Marchesoni F and Grigolini P 1984 Z. Phys. B 56 333
[25] Fox R F 1986 Phys. Rev. A 33 467
2011, Vol. 28 
