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According to the Langevin equation that describes the Brownian particle motion, the instantaneous power and average power of Brownian particle provided by periodic external force are analyzed. The mechanism of energy input to a bistable system to generate stochastic resonance is revealed. The theoretical analysis and numerical simulation manifest that the instantaneous power absorbed by Brownian particle changes periodically. The change frequency is twice that of periodical external force, and its amplitude and average are controlled by the noise intensity. The energy input form of periodic external force can be controlled effectively by changing the parameters of thermal environment where Brownian particle is located.
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Keywords:
- bistable system /
- stochastic resonance /
- stochastic energetic /
- instantaneous power
[1] Benzi R, Sutera A, Vulpiana A 1981 Phys. A 14 L453
[2] Gammaitoni L, Hanggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological 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)]
[4] Qin G R, Gong D C, Hu G and Wen X D 1992 Acta Phys. Sin. 41 360 (in Chinese) [秦光戎, 龚德纯, 胡岗, 温孝东 1992 物理学报 41 360]
[5] Zhu H J, Li R, Wen X D 2003 Acta Phys. Sin.52 2404 (in Chinese) [祝恒江, 李蓉, 温孝东 2003 物理学报 52 2404]
[6] Jin G X, Zhang L Y Cao L 2009 Chin. Phys. B 18 952
[7] Wang C J 2010 Chin. Phys. B 19 030503
[8] Dong X J 2010 Chin. Phys. B 19 010502
[9] Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118(in Chinese) [冷永刚, 王太勇, 郭焱, 汪文津, 胡世广2005 物理学报 54 1118]
[10] Lin M, Huang Y M 2007 Acta Phys. Sin. 56 6173 (in Chinese) [林敏, 黄咏梅 2007 物理学报 56 6173]
[11] Dong X J 2009 Chin. Phys. B 18 0070
[12] Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 物理学报 59 1494]
[13] Lin L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240 (in Chinese) [林灵, 闫勇, 梅冬成 2010 物理学报 59 2240]
[14] Guo Y FXu WWang L 2010 Chin. Phys. B 19 040503
[15] Zhang L Y, Jin G X, Cao L 2011 Acta Phys. Sin. 60 044207 (in Chinese) [ 张良英, 金国祥, 曹力 2011 物理学报 60 044207]
[16] Chen Z S Yang Y M 2011 Acta Phys. Sin. 60 074301 (in Chinese) [ 陈仲生, 杨拥民 2011 物理学报 60 074301]
[17] Sekimoto K 1998 Prog. Theor. Phys. Suppl. 130 17
[18] Iwai T 2001 Phys. A 300 350
[19] Dan D, Jayannavar A M 2005 Phys. A 345 404
[20] Saikia S, Roy R, Jayannavar A M 2007 Phys. Lett. A 369 367
[21] Sekimoto K 2007 Phys. Rev.Ｅ 76 060103(R)
[22] Seifert U 2008 Eur. Phys. J. B 64 423
[23] Lin M, Zhang M L 2011 Acta Phys. Sin. 60 020501 (in Chinese) [林敏, 张美丽 2011 物理学报 60 020501]
[24] Lin M, Zhang M L, Huang Y M 2011 Acta Phys. Sin. 60 080509(in Chinese) [林敏, 张美丽, 黄咏梅 2011 物理学报 60 080509]
[25] Scharton T D, Lyon R H 1968 J. Acoust. Soc. Am. 43 1332
[26] Xiong Y P, Xing J T, Price W G 2005 Proc. R. Soc. A 461 3381
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[1] Benzi R, Sutera A, Vulpiana A 1981 Phys. A 14 L453
[2] Gammaitoni L, Hanggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological 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)]
[4] Qin G R, Gong D C, Hu G and Wen X D 1992 Acta Phys. Sin. 41 360 (in Chinese) [秦光戎, 龚德纯, 胡岗, 温孝东 1992 物理学报 41 360]
[5] Zhu H J, Li R, Wen X D 2003 Acta Phys. Sin.52 2404 (in Chinese) [祝恒江, 李蓉, 温孝东 2003 物理学报 52 2404]
[6] Jin G X, Zhang L Y Cao L 2009 Chin. Phys. B 18 952
[7] Wang C J 2010 Chin. Phys. B 19 030503
[8] Dong X J 2010 Chin. Phys. B 19 010502
[9] Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118(in Chinese) [冷永刚, 王太勇, 郭焱, 汪文津, 胡世广2005 物理学报 54 1118]
[10] Lin M, Huang Y M 2007 Acta Phys. Sin. 56 6173 (in Chinese) [林敏, 黄咏梅 2007 物理学报 56 6173]
[11] Dong X J 2009 Chin. Phys. B 18 0070
[12] Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 物理学报 59 1494]
[13] Lin L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240 (in Chinese) [林灵, 闫勇, 梅冬成 2010 物理学报 59 2240]
[14] Guo Y FXu WWang L 2010 Chin. Phys. B 19 040503
[15] Zhang L Y, Jin G X, Cao L 2011 Acta Phys. Sin. 60 044207 (in Chinese) [ 张良英, 金国祥, 曹力 2011 物理学报 60 044207]
[16] Chen Z S Yang Y M 2011 Acta Phys. Sin. 60 074301 (in Chinese) [ 陈仲生, 杨拥民 2011 物理学报 60 074301]
[17] Sekimoto K 1998 Prog. Theor. Phys. Suppl. 130 17
[18] Iwai T 2001 Phys. A 300 350
[19] Dan D, Jayannavar A M 2005 Phys. A 345 404
[20] Saikia S, Roy R, Jayannavar A M 2007 Phys. Lett. A 369 367
[21] Sekimoto K 2007 Phys. Rev.Ｅ 76 060103(R)
[22] Seifert U 2008 Eur. Phys. J. B 64 423
[23] Lin M, Zhang M L 2011 Acta Phys. Sin. 60 020501 (in Chinese) [林敏, 张美丽 2011 物理学报 60 020501]
[24] Lin M, Zhang M L, Huang Y M 2011 Acta Phys. Sin. 60 080509(in Chinese) [林敏, 张美丽, 黄咏梅 2011 物理学报 60 080509]
[25] Scharton T D, Lyon R H 1968 J. Acoust. Soc. Am. 43 1332
[26] Xiong Y P, Xing J T, Price W G 2005 Proc. R. Soc. A 461 3381
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