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In this paper, we study the stochastic resonance in a piecewise nonlinear system driven by a periodic signal and colored noises, which is described by multiplicative and additive colored noises with colored cross-correlation. Using the two-state theory and the unified colored approximation, we can derive the analytical expressions of the steady-state probability density and the signal-to-noise ratio (SNR). Effects of colored noises and the periodic signal on SNR are presented. It is found that the conventional stochastic resonance and bona-fide stochastic resonance may exist in this system. Moreover, the value of the SNR peak decreases with increasing correlation time and correlation between the additive and multiplicative noises.
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Keywords:
- colored noise /
- a piecewise nonlinear system /
- stochastic resonance
[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2] Nicolis C, Nicolis G 1981 Tellus 33 225
[3] Gammaitoni L, Honggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[4] Honggi P, Talkner P, Borkovec M 1990 Rev. Mod. Phys. 62 251
[5] Calvo O, Mirasso C R, Toral R 2001 Electronics Lett. 37 1062
[6] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: ShanghaiScientific 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)]
[7] Yang J H, Liu X B 2010 Chaos 20 033124
[8] Xu C, Kang Y M 2011 Acta Phys. Sin. 60 108701 (in Chinese) [徐超, 康艳梅 2011 60 108701]
[9] Jung P, Honggi P 1987 Phys. Rev. A 35 4464
[10] Honggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
[11] Cao L, Wu D J 1995 Phys. Rev. E 52 3228
[12] Xie C W, Mei D C 2003 Chin. Phys. 12 1208
[13] Luo X Q, Zhu S Q 2003 Phys. Rev. E 67 021104
[14] Jin Y F, Xu W, Xu M, Fang T 2005 J. Phys. A 38 3733
[15] Jin Y F Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[16] Liu K H, Jin Y F 2013 Physica A 392 5283
[17] Xu Y, Gu R C, Zhang H Q, Xu W, Duan J Q 2011 Phys. Rev. E 83 056215
[18] Zhang H Q, Xu Y, Xu W, Li X 2012 Chaos 22 043130
[19] Wang K K, Liu X B 2014 Chin. Phys. B 23 010502
[20] Liang G Y 2003 Chin. Phys. 12 377
[21] Wang J, Cao L, Wu D J 2002 Chin. Phys. Lett. 19 1416
[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] Li B, Jin Y F 2013 Acta Phys. Sin. 62 150503 (in Chinese) [李贝, 靳艳飞 2013 62 150503]
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[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2] Nicolis C, Nicolis G 1981 Tellus 33 225
[3] Gammaitoni L, Honggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[4] Honggi P, Talkner P, Borkovec M 1990 Rev. Mod. Phys. 62 251
[5] Calvo O, Mirasso C R, Toral R 2001 Electronics Lett. 37 1062
[6] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: ShanghaiScientific 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)]
[7] Yang J H, Liu X B 2010 Chaos 20 033124
[8] Xu C, Kang Y M 2011 Acta Phys. Sin. 60 108701 (in Chinese) [徐超, 康艳梅 2011 60 108701]
[9] Jung P, Honggi P 1987 Phys. Rev. A 35 4464
[10] Honggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
[11] Cao L, Wu D J 1995 Phys. Rev. E 52 3228
[12] Xie C W, Mei D C 2003 Chin. Phys. 12 1208
[13] Luo X Q, Zhu S Q 2003 Phys. Rev. E 67 021104
[14] Jin Y F, Xu W, Xu M, Fang T 2005 J. Phys. A 38 3733
[15] Jin Y F Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[16] Liu K H, Jin Y F 2013 Physica A 392 5283
[17] Xu Y, Gu R C, Zhang H Q, Xu W, Duan J Q 2011 Phys. Rev. E 83 056215
[18] Zhang H Q, Xu Y, Xu W, Li X 2012 Chaos 22 043130
[19] Wang K K, Liu X B 2014 Chin. Phys. B 23 010502
[20] Liang G Y 2003 Chin. Phys. 12 377
[21] Wang J, Cao L, Wu D J 2002 Chin. Phys. Lett. 19 1416
[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] Li B, Jin Y F 2013 Acta Phys. Sin. 62 150503 (in Chinese) [李贝, 靳艳飞 2013 62 150503]
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