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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 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 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 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 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 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 57 0749]
[33] [34] [35] Hideo Hasegawa 2007 Physica A 384 241
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