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We study the motion of a particle in a bistable potential in the presence of single frequency signal and dual-frequency signal, and give the approximate analytical relationship between response peak-to-peak value and driven peak-to-peak value of the bistable system under the control of dual-frequency signal. The paper also reveals a peculiar phenomenon of the non-linear system, that is frequency coupling of different frequencies and the energy infiltration from the frequency of input to the other. The analysis is carried out from the view point of dynamics mechanism and the frequency spectrum distribution. It deepens the understanding of the mechanism of stochastic resonance in the bistable system. The results of numerical simulation prove the validity of theoretical analysis.
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Keywords:
- bistable system /
- frequency coupling /
- infiltration phenomenon /
- stochastic resonance
[1] ［1］Gammaitoni L， Hanggi P， Jung P， Marchesoni F 1998 Rev. Mod. Phys. 70 223
[2] ［2］Babinec P 1997 Phys. Lett. A 225 179
[3] ［3］Nozaki D, Mar D J, Grigg P ， Collins J J 1999 Phys. Rev. Lett. 82 2402
[4] ［4］Qin G R, Gong D C, Hu G， Wen X D 1992 Acta Phys. Sin. 41 360 (in Chinese)［秦光戎、龚德纯、胡岗、温孝东 1992 41 360］
[5] ［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 52 2404］
[6] ［6］Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)［林敏、黄咏梅 2006 55 3277］
[7] ［7］Jin Y F， Xu M， Fang T 2005 J. Phys. A 38 3733
[8] ［8］Guo F， Zhou Y R， Jiang S Q， Gu T X 2006 Chin. Phys. 15 947
[9] ［9］Berdichevsky V， Gitterman M 1999 Phys. Rev. E 60 1494
[10] ］Dan D， Jayannavar A M 2005 Physica A 345 404
[11] ］Lin M, Mao Q M, Zheng Y J, Li D S 2007 Acta Phys. Sin. 56 5021 (in Chinese)［林敏、毛谦敏、郑永军、李东升 2007 56 5021］
[12] ］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)］
[13] ］Lin M， Fang L M 2009 Acta Phys. Sin. 58 2136 (in Chinese) ［林敏、方利民 2009 58 2136］
[14] ］Wang J F， Liu F， Wang J Y， Chen G， Wang W 1997 Acta Phys. Sin. 46 2305 (in Chinese) ［王嘉赋、刘锋、王均义、陈光、王炜 1997 46 2305］
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[1] ［1］Gammaitoni L， Hanggi P， Jung P， Marchesoni F 1998 Rev. Mod. Phys. 70 223
[2] ［2］Babinec P 1997 Phys. Lett. A 225 179
[3] ［3］Nozaki D, Mar D J, Grigg P ， Collins J J 1999 Phys. Rev. Lett. 82 2402
[4] ［4］Qin G R, Gong D C, Hu G， Wen X D 1992 Acta Phys. Sin. 41 360 (in Chinese)［秦光戎、龚德纯、胡岗、温孝东 1992 41 360］
[5] ［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 52 2404］
[6] ［6］Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)［林敏、黄咏梅 2006 55 3277］
[7] ［7］Jin Y F， Xu M， Fang T 2005 J. Phys. A 38 3733
[8] ［8］Guo F， Zhou Y R， Jiang S Q， Gu T X 2006 Chin. Phys. 15 947
[9] ［9］Berdichevsky V， Gitterman M 1999 Phys. Rev. E 60 1494
[10] ］Dan D， Jayannavar A M 2005 Physica A 345 404
[11] ］Lin M, Mao Q M, Zheng Y J, Li D S 2007 Acta Phys. Sin. 56 5021 (in Chinese)［林敏、毛谦敏、郑永军、李东升 2007 56 5021］
[12] ］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)］
[13] ］Lin M， Fang L M 2009 Acta Phys. Sin. 58 2136 (in Chinese) ［林敏、方利民 2009 58 2136］
[14] ］Wang J F， Liu F， Wang J Y， Chen G， Wang W 1997 Acta Phys. Sin. 46 2305 (in Chinese) ［王嘉赋、刘锋、王均义、陈光、王炜 1997 46 2305］
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