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研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中, 噪声强度和相关时间对平均首次穿越时间的影响. 利用一致有色噪声近似方法和最速下降方法, 推导出系统平均首次穿越时间的表达式. 研究结果表明: 系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构, 即“共振”现象, 峰值会随着加性噪声强度和噪声之间关联强度的增加而减小. 而平均首次穿越时间作为加性噪声的函数呈单调曲线, 说明乘性噪声和加性噪声对平均首次穿越时间的影响不同. 此外, 乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时 对系统平均首次穿越时间的影响是不同的.In this paper, We have studied the effects of intensity and correlation time of noises on the mean first-passage time in a picecewise nonlinear system driven by multiplicative and additive colored noises with colored cross-correlation. We derived the expression of the mean first-passage time (MFPT) by applying the unified colored approximation method and the steepest-descent approximation. Results show that the MFPT of the system exhibits a mono-peak structure and the “resonance” phenomena enhance with the increase of multiplicative noise intensity. The value of the peak decreases with increasing additive noise intensity and the correlation between the additive and multiplicative noises. However, the MFPT of the system increases with the increase of additive noise intensity. That is, the effects of the additive noise and the multiplicative noise on MFPT are different. Moreover, the negative and passive correlations play different roles in the MFPT.
[1] Reimann P 1995 Phys. Rev. Lett. 74 4576
[2] Li J H, Hu B, Xing D Y, Dong J M 1999 Phys. Rev. E 60 6443
[3] Madureira A J R, Hanggi P, Wio H S 1996 Phys. Lett. A 271 248
[4] Wang J, Cao L, Wu D J 2003 Phys. Lett. A 308 23
[5] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technoogical 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)]
[6] Jin Y F, Xu W, Ma S J, Li W 2005 Acta Phys. Sin. 54 3480 (in Chinese) [靳艳飞, 徐伟, 马少娟, 李伟 2005 54 3480]
[7] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
[8] Fox R F 1986 Phys. Rev. A 34 4525
[9] Jung P, Hanggi P 1987 Phys. Rev. A 35 4464
[10] Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[11] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[12] Liang G Y, Cao L, Wu D J 2002 Phys. Lett. A 294 190
[13] Liang G Y, Cao L, Wu D J 2004 Physica. A 335 371
[14] Luo X Q, Zhu S Q 2003 Phys. Rev. E 67 021104
[15] Jin Y F, Xu W, Li W, Ma S J 2005 Journal of Dynamics and Control 3 60 (in Chinese) [靳艳飞, 徐伟, 李伟, 马少娟 2005 动力学与控制学报 3 60]
[16] Jin Y F, Xu W 2005 Chaos Solitons & Fractals 23 275
[17] Zhang X Y, Xu W, Zhou B C 2009 Commun Nonlinear Sci. Numer. Simulat. 14 4220
[18] Ning L J, Xu W, Yang X L 2007 Acta Phys. Sin. 56 6809 (in Chinese) [宁丽娟, 徐伟, 杨晓丽 2007 56 6809]
[19] Hu H Y 1996 Acta Mech. Sin. 28 483 (in Chinese) [胡海岩 1996 力学学报 28 483]
[20] Hu H Y 1995 Vibr. Eng. Journal. 8 331 (in Chinese) [胡海岩 1995 振动工程学报 8 331]
[21] Liang G Y 2003 Chin. Phys. 12 0377
[22] You J Y, Cao L, Ke S Z, Wu D J 2001 Eur. Phys. J. B 20 397
[23] Xie C W, Mei D C, Wu D J 2003 Eur. Phys. J. B 33 83
[24] Fiasconaro A, Spagnolo B 2011 Phys. Rev. E 83 041122
[25] Simpson D J W, Kuske R 2011 Physica D 240 1189
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[1] Reimann P 1995 Phys. Rev. Lett. 74 4576
[2] Li J H, Hu B, Xing D Y, Dong J M 1999 Phys. Rev. E 60 6443
[3] Madureira A J R, Hanggi P, Wio H S 1996 Phys. Lett. A 271 248
[4] Wang J, Cao L, Wu D J 2003 Phys. Lett. A 308 23
[5] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technoogical 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)]
[6] Jin Y F, Xu W, Ma S J, Li W 2005 Acta Phys. Sin. 54 3480 (in Chinese) [靳艳飞, 徐伟, 马少娟, 李伟 2005 54 3480]
[7] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
[8] Fox R F 1986 Phys. Rev. A 34 4525
[9] Jung P, Hanggi P 1987 Phys. Rev. A 35 4464
[10] Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[11] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[12] Liang G Y, Cao L, Wu D J 2002 Phys. Lett. A 294 190
[13] Liang G Y, Cao L, Wu D J 2004 Physica. A 335 371
[14] Luo X Q, Zhu S Q 2003 Phys. Rev. E 67 021104
[15] Jin Y F, Xu W, Li W, Ma S J 2005 Journal of Dynamics and Control 3 60 (in Chinese) [靳艳飞, 徐伟, 李伟, 马少娟 2005 动力学与控制学报 3 60]
[16] Jin Y F, Xu W 2005 Chaos Solitons & Fractals 23 275
[17] Zhang X Y, Xu W, Zhou B C 2009 Commun Nonlinear Sci. Numer. Simulat. 14 4220
[18] Ning L J, Xu W, Yang X L 2007 Acta Phys. Sin. 56 6809 (in Chinese) [宁丽娟, 徐伟, 杨晓丽 2007 56 6809]
[19] Hu H Y 1996 Acta Mech. Sin. 28 483 (in Chinese) [胡海岩 1996 力学学报 28 483]
[20] Hu H Y 1995 Vibr. Eng. Journal. 8 331 (in Chinese) [胡海岩 1995 振动工程学报 8 331]
[21] Liang G Y 2003 Chin. Phys. 12 0377
[22] You J Y, Cao L, Ke S Z, Wu D J 2001 Eur. Phys. J. B 20 397
[23] Xie C W, Mei D C, Wu D J 2003 Eur. Phys. J. B 33 83
[24] Fiasconaro A, Spagnolo B 2011 Phys. Rev. E 83 041122
[25] Simpson D J W, Kuske R 2011 Physica D 240 1189
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