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Making use of the unified colored noise approximation, the steady sate characteristics of the one-dimension of FitzHugh-Nagumo neural system with two different colored noises are investigated. The expressions of the steady state probability distribution function and the mean value are obtained. After numerical calculation, the results show that the self-correlated time of the multiplicative noise 1, the self-correlated time of the additive noise 2,the intensity of the additive noise , and the intensity of the multiplicative noise D can induce the transition. The increases of and D are conductive to the switch from the exciting state to the resting state. However, with 1 and 2 increasing, the switch from the resting state to the exciting state becomes obvious. The noise intensity and it self-correlated time play opposite roles.
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Keywords:
- FHN neural system /
- colored noise /
- steady state probability distribution function /
- mean value
[1] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai scienti?c and Technological Education Press) (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)]
[2] Moss F, McClintock P V E 1998 Noise in Nonlinear Dynamical Systems (Cambridge: Cambridge University Press) Vol.1--3
[3] Liu Q, Jia Y 2004 Phys. Rev. E 70 041907
[4] Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese) [王参军, 梅冬成2008 57 3983]
[5] Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 61 010503]
[6] Braun H A, Wissing Schafer H K, Hirsch M C 1994 Nature 367 270
[7] Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[8] Mei D C, Xie C W, Zhang L 2004 Eur. Phys. J. B 41 107
[9] Wang C J, Wei Q, Mei D C 2008 Phys. Lett. A 372 2176
[10] Wang C J, Wei Q, Zheng B B 2008 Acta Phys. Sin. 57 1735 (in Chinese) [王参军, 魏群, 郑宝兵2008 57 1735]
[11] Nie L R, Mei D C 2008 Phys. Rev. E 77 031107
[12] Alarcón T, Pérez Madrid A, Rubí J M 1998 Phys. Rev. E 57 4979
[13] Yu S N,Jia Y 2000 Journal of Central China Normal University (Nature Science) 34 281
[14] 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]
[15] 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]
[16] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[17] Sancho J M, San Miguel M, Katz S L and Gunton J D 1982 Phys. Rev. A 26 1589
[18] Wang C J 2008 Chin. Phys. B 17 479
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[1] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai scienti?c and Technological Education Press) (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)]
[2] Moss F, McClintock P V E 1998 Noise in Nonlinear Dynamical Systems (Cambridge: Cambridge University Press) Vol.1--3
[3] Liu Q, Jia Y 2004 Phys. Rev. E 70 041907
[4] Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese) [王参军, 梅冬成2008 57 3983]
[5] Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 61 010503]
[6] Braun H A, Wissing Schafer H K, Hirsch M C 1994 Nature 367 270
[7] Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[8] Mei D C, Xie C W, Zhang L 2004 Eur. Phys. J. B 41 107
[9] Wang C J, Wei Q, Mei D C 2008 Phys. Lett. A 372 2176
[10] Wang C J, Wei Q, Zheng B B 2008 Acta Phys. Sin. 57 1735 (in Chinese) [王参军, 魏群, 郑宝兵2008 57 1735]
[11] Nie L R, Mei D C 2008 Phys. Rev. E 77 031107
[12] Alarcón T, Pérez Madrid A, Rubí J M 1998 Phys. Rev. E 57 4979
[13] Yu S N,Jia Y 2000 Journal of Central China Normal University (Nature Science) 34 281
[14] 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]
[15] 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]
[16] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[17] Sancho J M, San Miguel M, Katz S L and Gunton J D 1982 Phys. Rev. A 26 1589
[18] Wang C J 2008 Chin. Phys. B 17 479
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