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研究了非高斯噪声激励下含周期信号的FHN模型的动力学行为. 通过计算神经元的平均响应时间、观察神经元的共振活化和噪声增强稳定现象,分析了非高斯噪声对神经元动力学行为的影响. 发现通过改变非高斯噪声的相关时间可以有效地改变共振活化和噪声增强稳定现象. 观察到在强相关噪声下不同强度的非高斯噪声抑制了神经元的噪声增强稳定现象而共振活化现象几乎不变,也就是非高斯噪声有效地增强了神经响应的效率. 观察了平均响应时间与非高斯噪声参数q之间的关系,当q为一个有限的小于1的值时,平均响应时间取得最小值. 最后表明在一定条件下,非高斯噪声出现重尺度现象,即非高斯噪声产生的效果可以由高斯白噪声来估计.The dynamics of the FitzHugh-Nagumo (FHN) model in the presence of non-Gaussian noise and a periodic signal is analyzed in this paper. We observe the resonant activation (RA) and the noise enhanced stability (NES) phenomena and analyze the effect of the non-Gaussian noise on the neuron dynamics by the mean response time (MRT) of the neuron. Some significant changes of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise are found. We observe that the NES effect is suppressed and RA phenomenon is unchanged, i.e., the non-Gaussian noise effectively enhances the efficiency of the neuronal response, for the case of strongly correlated noise. We report on the MRT as a function of q, and find that MRT is nonmonotonicaly dependent on q with a minimum at a finite q value which is smaller than 1. Finally we obtain that in certain situations, the non-Gaussian noise causes rescaling phenomenon, then the effect of non-Gaussian noise can be reproduced by a white noise.
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Keywords:
- FitzHugh-Nagumo neural system /
- non-Gaussian noise /
- mean response time /
- resonant activation phenomena
[1] Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵 燕、 徐 伟、 邹少存 2009 物理学报 58 1396]
[2] [3] McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[4] [5] Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123
[6] Zhang G J, Xu J X 2005 Acta Phys. sin. 54 557 (in Chinese) [张广军、 徐健学 2005 物理学报 54 557]
[7] [8] [9] Magnasco M O 1993 Phys. Rev. Lett. 71 1477
[10] [11] Doering C R, Horsthemke W, Riordan J 1994 Phys. Rev. Lett. 72 2984
[12] Broeck C V D, Parrondo J M R, Toral R 1994 Phys. Rev. Lett. 73 3395
[13] [14] [15] Castro F, Sanchez A D, Wio H S 1995 Phys. Rev. Lett. 75 1691
[16] [17] Doering C R, Gadoua J C 1992 Phys. Rev. Lett. 69 2318
[18] Dayan I, Gitterman M, Weiss G H 1992 phys. Rev. A 46 757
[19] [20] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[21] [22] FitzHugh R 1961 Biophys J. 1 445
[23] [24] Valenti D, Augello G, Spagnolo B 2008 Eur. Phys. J. B 65 443
[25] [26] Tuckwell H C, Roger Rodriguez, Wan F Y M 2003 Neural Computation 15 143
[27] [28] Acebron J A, Bulsara A R, Rappel W J 2004 phys. Rev. E 69 026202
[29] [30] Hiroyuki Kitajima, Jrgen Kurths 2005 Chaos 15 023704
[31] [32] Wang C Q, Xu W, Zhang N M, Li H Q 2008 Acta Phys. sin. 57 0749 (in Chinese) [王朝庆、 徐 伟、 张娜敏、 李海泉 2008 物理学报 57 0749]
[33] [34] [35] Hideo Hasegawa 2007 Physica A 384 241
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[1] Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵 燕、 徐 伟、 邹少存 2009 物理学报 58 1396]
[2] [3] McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[4] [5] Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123
[6] Zhang G J, Xu J X 2005 Acta Phys. sin. 54 557 (in Chinese) [张广军、 徐健学 2005 物理学报 54 557]
[7] [8] [9] Magnasco M O 1993 Phys. Rev. Lett. 71 1477
[10] [11] Doering C R, Horsthemke W, Riordan J 1994 Phys. Rev. Lett. 72 2984
[12] Broeck C V D, Parrondo J M R, Toral R 1994 Phys. Rev. Lett. 73 3395
[13] [14] [15] Castro F, Sanchez A D, Wio H S 1995 Phys. Rev. Lett. 75 1691
[16] [17] Doering C R, Gadoua J C 1992 Phys. Rev. Lett. 69 2318
[18] Dayan I, Gitterman M, Weiss G H 1992 phys. Rev. A 46 757
[19] [20] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[21] [22] FitzHugh R 1961 Biophys J. 1 445
[23] [24] Valenti D, Augello G, Spagnolo B 2008 Eur. Phys. J. B 65 443
[25] [26] Tuckwell H C, Roger Rodriguez, Wan F Y M 2003 Neural Computation 15 143
[27] [28] Acebron J A, Bulsara A R, Rappel W J 2004 phys. Rev. E 69 026202
[29] [30] Hiroyuki Kitajima, Jrgen Kurths 2005 Chaos 15 023704
[31] [32] Wang C Q, Xu W, Zhang N M, Li H Q 2008 Acta Phys. sin. 57 0749 (in Chinese) [王朝庆、 徐 伟、 张娜敏、 李海泉 2008 物理学报 57 0749]
[33] [34] [35] Hideo Hasegawa 2007 Physica A 384 241
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